







An octagonal pool deck 
20200530 

From lauchie: need help on cut sizes and cut degrees on octagon pool deck for a 24 foot round pool Answered by Harley Weston. 





An isosceles triangle 
20200416 

From jo: Find the angle between the two sides of length 5 in an isosceles triangle that has one side of length 9 and two sides of length 5. Answered by Penny Nom. 





The side length of a hexagon 
20200205 

From Rob: I have a hexagon that is 8 feet wide how long would the sides be? Answered by Penny Nom. 





The angle of a countersunk screw 
20200119 

From Barbie: I need to be able to verify the angle used for the head of a countersunk screw.
I have the diameter of the head, diameter of the shank and height between the
two. I assume it would be considered a frustum.
For example:
A standard 90 degree metric flat head screw in an M2 diameter has a head diameter of 3.65mm,
the actual thread diameter is 1.98mm and the height of the head is 1.20mm.
How can I prove that it is a 90 degree angle? Answered by Harley Weston. 





Volume of a tree 
20191219 

From Maria: I have trees for sale. I need to calculate the volume of a tree from base which is wider than the stem.The base will be used for the making of hurleys, similar to hockey sticks so the wider base is crucial. Answered by Penny Nom. 





A hexagonal planter 
20191119 

From Colleen: I need to build a hexagon planter around a 32” square box. How long is each side of the hexagon? Answered by Penny Nom. 





A tube through a board at 45 degrees 
20190615 

From Guy: I need to insert a tube 5/8" diameter into a board at a 45 degree angle. What size hole must I drill for the tube to fit snugly? Answered by Harley Weston. 





Subdividing land 
20190509 

From Reuben: This is the measurements of my plot, AB 46.7M, BC 193.1, CD 198.5 & DA 208.25 (Clockwise naming of sides) angle A at 90 degrees. My questions is how do i subdivide this plot from the bottom having lines running parallel to CD, eg two 2acre plots. the the remaining part becomes my compound (Uper part at line AB) Answered by Harley Weston. 





A circle with a circular hole 
20190311 

From Sue: My little one is wondering if a circle with a circular hole could be described as an irregular semicircle.
As it has 2 sides but is not the standard shape. Could you share your thoughts ?? Answered by Penny Nom. 





7 spheres on a hexagonal tray 
20190114 

From herm: what is the length of each side of a hexagonal tray, with the height of each side 0.75 inch, to hold seven spheres, each with a diameter of 3.00 inches? The spheres are placed such that each side of the hexagon is touched by one sphere at its midpoint (and the seventh sphere is place in the center of the "ring" of the other six spheres. Answered by Harley Weston. 





A quadrilateral inside a square 
20190102 

From Swetha: In 2*2 square ABCD, E is the mid point of the side AD. F is a
point in BE.CF is perpendicular to BE. Find the area of the quadrilateral CDEF Answered by Penny Nom. 





A rectangle problem 
20190101 

From ahamed: In rectangle ABCD, angle BCD is trisected. CE,CF meet the sides AB,AD at E,F. BE=6cm, AF=2cm so, find the area of the rectangle ABCD? Answered by Penny Nom. 





Two intersecting tubes 
20180815 

From Tommy: Hi, I am trying to determine a mathematical model for two metal tubes joining at various degrees for weld.
For instance, if I am trying to join the end of a tube to the side of another at a 90 degree angle, it will be a simple profile cut out of the joining tube.
Where it gets tricky is if you want to join the new tube at a given angle.
It would be very helpful if you could give insight as to how I can solve this problem or an equation I could work off of.
Thanks for the help!! Answered by Edward Doolittle. 





The volume of a berm 
20180604 

From Mike: Have a berm that is 700’ long, 29’ y’all and needs a 20’ top with 51 slope on one side and 31 slope in the other Answered by Penny Nom. 





A circle inscribed in a quarter circle 
20180416 

From abhijeet: ABC is a quarter circle and a smaller circle is inscribed in it. if AB = 1cm then find the radius of smaller circle Answered by Penny Nom. 





A square inside a circle inside a square 
20161113 

From Jeff: Greetings,
I came across a question from a textbook from years ago. I've been trying to solve it, but am not sure if my approach is correct.
There are 2 squares (1 inner, 1 outer) & 1 circle.
The inner square is the largest square that will fit inside the circle. It has an area of 1 unit.
The circle is the biggest that will fit in the outer square.
What is the area of the outer square? Answered by Penny Nom. 





Volume of liquid remaining in a tilted cylinder 
20161108 

From Brian: I am trying to determine the amount of a liquid remaining in a 55 gallon drum when it is tilted at 45 degrees and the liquid level is low enough so that the liquid does not completely cover the bottom of the drum.
Your help is greatly appreciated. Answered by Harley Weston. 





A deck that is half an ellipse 
20160228 

From Steve: On your website, I was reading a question and your response from a girl named Angela in which you provided a formula by which her father, a welder, could figure out points on an arc corresponding to equal 3' intervals on a 30' chord where the vertex was 1' off the chord. Is there an equivalent formula when working with an ellipse? I suspect this change will make the calculations significantly more complex. I am building a deck that is half an oval, and would like to be able to mark out the perimeter by measuring the distance from regular intervals on the primary access to a corresponding point on the perimeter. I will then connect the points on the perimeter and cut a reasonably smooth arc. The length of the primary access will be 22' and width of the deck at the vertex is 9'. I would like to be able to know the distance from the primary axis to a point on the perimeter at equal intervals of 6" along the primary axis. Can you help? Answered by Penny Nom. 





The sum of the angles of a triangle 
20160224 

From Sophia: Does every triangle add up to 180 degrees? (Such as a unique triangle) Answered by Penny Nom. 





Filling a pool with dirt 
20150501 

From Mike: I have a hole which a 24 ft pool in it is 10" deep in the the centre and goes to 1" inch at the edge want to fill it in with dirt how many yards of dirt would I need to fill it in Answered by Penny Nom. 





A wireless fence 
20150418 

From Dave: I'm buying a wireless fence to keep my pet in my yard. It has a half acre range. In a straight line how far would that be? Answered by Penny Nom. 





Bricks around a fire pit 
20150305 

From Jayson: I have a round fire pit. It measures 25 inches in diameter. I have 12 inch long square bricks to go around it . My question is what degree do I cut the ends of these bricks to make them fit around this circle? The brick dimensions are 12"Lx6"Wx4"D. Answered by Harley Weston. 





An isosceles triangle and an arc 
20150218 

From Sreeharsha: The diagram shows an isosceles triangle ABC in which BC = AC = 20 cm, and angle BAC = 0.7
radians. DC is an arc of a circle, centre A. Find, correct to 1 decimal place,
(i) the area of the shaded region, [4]
(ii) the perimeter of the shaded region. [4] Answered by Penny Nom. 





Some geometry problems 
20141107 

From Maria: Hi there,
My name is Maria and I'm a student in Ireland.
Can you pleeeease help me with questions 1 to 4 on the attached file. I'm really stuck: Answered by Penny Nom. 





Cutting a round cake so that it doesn't dry out 
20140826 

From James: I'm wondering if there's a simple way to calculate the area between two parallel chords of a circle equidistant from its diameter, or if I have the area, to find the distance between the two chords.
Here's my "problem". You may have heard of the way of cutting a round cake so that it doesn't dry out  make two parallel cuts (chords) the length of the cake, take the middle piece, then push the two pieces together.
So I know the area of a 12" cake, and I want say, exactly an eighth of the cake. How wide do I cut the centre piece?
Now to get even more difficult, the next day I want another eighth from the centre. How wide do I cut the next pieces, and so on...?
Thanks,
James Answered by Harley Weston. 





An oval pool 
20140621 

From steve: I have a 16' x 28' oval pool that is buried 24" deep inground. The dig site is dug
2' wider all the way around the pool. I need to back fill this area with stone. I want to fill this area with 6 to 8"
of stone. How many tons of stone will this take?
Thanks you
Steve Answered by Penny Nom. 





An octagonal pad 
20140425 

From George: Hi,
I need to pour a cement pad in the shape of an octagon that allows
for 12" of clearance around the tank I will be putting on it.
The tank has a radius of 16'. Answered by Penny Nom. 





A circle is divided into three sectors 
20140417 

From atolagbe: the area of a circle is 154cm square. it is divided into three sectors such that two of the sectors are equal in size and the third sector is three times the size of the other two put together. calculate the perimeter of the third sector. take pi=22/7? Answered by Penny Nom. 





A sand trench around a pool 
20140413 

From steve: How sand is needed to back fill a trench around a 24ft dia. pool that is 26" deep by 2ft wide. Making the outside dia. 26ft.
Thank You Answered by Penny Nom. 





Cutting a hexagon from a disk 
20140405 

From Paul: I am a machinist and sometimes need to make a hex from
round material.
If I know the distance of the flat sides opposite one another
of my hex, how can I calculate the size of material I need to turn
to give me the right diameter to finish the part with six sides? Answered by Penny Nom. 





The area of a 5 sided lot 
20140315 

From Michael: Question from michael:
This lot is in feet. 59x154x109x188x137 per the plot plan Answered by Harley Weston. 





Rolls of window film 
20140214 

From Travis: This question is probably close to the same question as "roll of paper"
We have Rolls of Window Film that we are trying to figure out an equation for a spreadsheet that we can use to "inventory" our window film.
We use a caliper tool to measure the thickness of the roll in millimeters.
the core thickness = 1.90mm
Full Roll thickness(including core) = 9.08mm to 9.12mm
Film thickness = 0.06
Full Roll of Film is supposed to average 1200" of film
What equation could we use to get the approximate inches left remaining on the roll if we measured the roll including the core with the Caliper tool in Millimeters? Answered by Harley Weston. 





Analytic Geometry 
20131218 

From fRitz: if (x,4) is equidistant from (5,2) and (3,4), find x. Answered by Penny Nom. 





conical lamp stand/staved wood 
20131207 

From Henry: need to make lamp stand that is wooden staved; need it to be 25 inches at bottom and 10 inches at top; need to know angles for staves to be cut; the lamp stand will be rounded on a lathe and will be 40 inches tall John Lucas built one and it is pictured on his web page. thank you for any help/direction; I checked out the answered for cone shaped objects on your page but didn't find what I could use. thanks again. Henrywoodturner, parent teacher student . . . . . Answered by Harley Weston. 





2 concentric circles 
20131127 

From Dimaris: The radius of the outer circle of 2 concentric circles is x. An
equilateral triangle inscribed in the outer circle also circumscribes the
inner circle. What is the radius of the inner circle in terms of x? Answered by Penny Nom. 





A square inscribed in a circle 
20131014 

From Jenn: Hello! I am about to buy a 7'9" round rug, but I want to have it cut down into a square. What's the largest square I can obtain from this? Thank you! Answered by Penny Nom. 





Euclid's Parallel Postulate 
20130820 

From Justin: Hello there,
I was wondering is Euclid's Fifth Parallel Postulate of parallel lines never intersecting, undecidable or essentially undecidable?
Thank you so much for any help you can provide! Answered by Robert Dawson. 





Dirt to fill a pool 
20130713 

From Neil: I had a 24 foot diameter pool. The perimeter of it was at ground
level. The pool sloped 1 foot deeper to the middle. In other
words "a 1 ft. dish. How many cubic yards of dirt do I need to
fill this hole? Answered by Penny Nom. 





A gravel pile in the shape of a triangular pyramid 
20130404 

From Casey: Hello
Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it.
I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away.
I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion.
Thank you for any help.
Casey Answered by Penny Nom. 





Question 
20130404 

From Casey: Hello
Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it.
I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away.
I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion.
Thank you for any help.
Casey Answered by Penny Nom. 





A geometry word problem 
20130124 

From Matthew: "G", "A" and "B" are collinear. "A" is between "G" and "B". "GA" Is 14 less than 3 times "AB". "GB"=46 Find "GA"
How would you solve this? Answered by Penny Nom. 





A label to cover a plastic cup 
20121023 

From Kevin: I'm trying to make a label to cover the entire outer area or a plastic cup. I know there must be a way to figure out the dimensions needed, but I can't seem to figure it out. The circumference of the bottom of the cup is 21.4cm and the circumference at the top of the cup is 29.8cm. The cup is 14.5cm tall. What should the height of the arc from the plane connecting the two ends of the 21.4cm arc. I attached a diagram where x is the value I'm looking for. I'm guessing there is some simple relationship between the length of a line and the arc needed to turn that line into a perfect circle, but I don't know what it is. Can you figure this out and share it with me? Thanks.
Kevin Answered by Penny Nom. 





A question about a parallelogram 
20121014 

From Renu: Question from renu, a parent:
ABCD is a parallelogram. BP and DQ are two parallel lines cutting AC at P and Q respectively. prove that BPDQ is a parallelogram Answered by Harley Weston. 





A tank with an inner walled compartment 
20121012 

From don: I have a tank 20 feet diameter, 19' 8" tall with an inner walled compartment that has a 7' 6" radius arc with in the tank. I need to figure out the volume of the inner area and the volume of the larger area. Answered by Harley Weston. 





Making a wind sock 
20120828 

From John: I am trying to build a wind sock and need to be able to lay the shape
out on cloth. I need the wind sock front opening (diameter) to be
3 1/2" and the rear opening diameter to be 1". The windsock needs
to be 9 1/2" long. I tried using the example of the person trying to
make a crayfish trap but got confused and could not figure out my
numbers. Any help would be greatly appreciated.
Thanks
John Answered by Penny Nom. 





A tangent line to a circle 
20120414 

From Novelyn: find an equation of the line tangent to a circle with equation x^2+y^2+6x8y27=0 at the point P(1,2) Answered by Penny Nom. 





Measuring the liquid in a horizontal tank 
20120228 

From Philip: I have a steel gas tank that is 3' dia X 5' length. The total volume is 1000 litres.
But how much is left when I use a stick and measure 6" from the bottom or 12" or 24" ??
Is there a formula to use for this task?
Thanks. Answered by Harley Weston. 





Building a tipi 
20120129 

From Lacy: Hi there!
We are building a tipi for our children. We want to build a large one about 15ft tall with a base of about 15 feet diameter. I am trying to figure out how much canvas we need to accomplish this. I graduated about 20 years ago and am struggling. Please help if you can. Answered by Penny Nom. 





The volume of a dugout 
20120128 

From Jan: is there a formula for calculating the cubic yardage removed from a dugout
for example that is forty feet wide by one hundred and twenty feet long by
twelve feet deep with a three to one slope? It is the slope that makes it a
little tricky. Thank you. Answered by Penny Nom. 





Great circle course 
20120125 

From Hervé: On the earth, the mathematical formula giving the distance
between two points, and the initial course for a boat on the great circle
is well known.
I need to find the inverse formula, ie knowing an initial position on earth,
and the initial course of the boat, and the distance to run on the great circle,
the formula gives the final position (longitude and latitude). Answered by Robert Dawson. 





An equilateral triangle and some circles 
20120110 

From tushar: draw an equilateral triangle with side 6cm.draw 3circles with radii 3cm on each angular point of triangle.draw common tangent on each of two circles Answered by Penny Nom. 





Two circles 
20111204 

From Luke: Two fixed circles intersect at A and B.
P is a variable point on one circle.
PA and PB when produced meet the other circle at M and N respectively.
Prove that MN is of constant length.
Thanks!
p.s. I also sent the question with a figure via email. Answered by Chris Fisher. 





A triangle problem 
20111120 

From May: In triangle ABC, AB=AC, angle A=20,
D lie on AB making DC=AD,
E lie on AC making angle EBC=70.
Find angle DEB. Answered by Chris Fisher. 





A vector geometry problem 
20111028 

From aishwarya: hi...my name is Aishwaarya and i am a student from India..
My problem is in vector geometry which i am sending u my an attachment
including a diagram..
Thanks
Aishwarya Answered by Chris Fisher. 





A mythical soccer ball 
20111027 

From Joel: We've been working on this problem diligently and can't seem to come up with the answer book's answer. We think it may be wrong, yet want to check it with an expert. Here goes.
The school's new soccer balls are covered with 64 regular hexagonal panels. Each hexagon measures 2 inches between opposite corners and 1.5 inches between opposite sides. What is the total surface area of the soccer ball? Answered by Robert Dawson and Lorraine Dame. 





Building a custom range hood 
20111008 

From Bill: I'm building a custom range hood for a customer with special order material that matches
their newly installed cabinets and I need it to be perfect. The hood is basically a pyramid
but the 4th side is the flat wall at the back and a flat, rectangular top. I need to calculate
the bevel and miter of the three sides but I never was very good with geometry functions
(although I am fairly good with other math fields). I either need the calculations from you
at least (shudder) a formula or set of formulas so that I can calculate them myself. Answered by Harley Weston. 





Geometry Related Careers 
20110901 

From Richard: Good morning,
I am hoping to find a list of careers that would relate to geometric constructions and tessellations.
I have searched the internet some and some of the sites I have found are a bit questionable or dated. Are there sites that Math Central would recommend?
I could not find anything when I did a search on the site.
Thanks in advance,
RVD Answered by Walter Whiteley. 





The length of a belt around three pulleys 
20110518 

From Grant: I need to calculate the belt length around these pulleys, please can you
help or refer me?
Known variables
D  Large Pulley Diameter
d  Small Pulley Diameter
c  Center Distance between D and d
T  Tension Pulley Diameter
x  Horizontal Distance between T and d' Centers
y  Vertical Distance between T and d's Centers
I need to calculate the belt length around these pulleys.
Kind Regards,
Grant Answered by Harley Weston. 





The length of a chord 
20110425 

From G: A 120 degree central angle intercepts a circle at the points A and B. The radius of the circle is 10 cm. Find the length of chord AB. Answered by Penny Nom. 





A circle in a square in a circle in a square 
20110329 

From George: A circle within a square which is inside
a larger circle which is also within a square.
(a circle in a square inside a circle in a square)
Equation of the smaller circle is: x ^ 2 x y ^ 2 = 25.
What are the dimensions of the larger square?
Been 40 years, trying to help my son. Answered by Penny Nom. 





A geometry problem 
20110325 

From eujane: in triangle ABC in which AB=12,BC=18,&Ac=25, a semicircle is drawn so that its diameter lies on AC and so that it is tangent to AB and BC.if O is the center of the circle, find the measure of OA.9 Answered by Chris Fisher. 





Calibrating a conical tank 
20110205 

From Bill: Hi, I have a round tank with tapered sides where I know the diameter at the top and bottom. Is there a formula I can use to calculate the volume by measuring from the bottom up the side (at the angle of the side) to any given point? Thanks, Bill Answered by Stephen La Rocque and Penny Nom. 





A fence around a water tank 
20110201 

From Heath: I am building a fence around a water tank. the fence is to be in the shape of a normal octagon. The tank has a circumference of 57 ' 6''. I would like the fence to be 3 ft from the tank at the skinny point . How would I calculate(for the simple guy) where to set each of my 4x4 posts at the 8 corners. Any help would be greatly appreciated. Answered by Harley Weston. 





Points with distance 5 from the point (2, 1) 
20110119 

From Alexa: Find all points having a xcoordinate of 2 whose distance from the point (2, 1) is 5. Answered by Penny Nom. 





The angle between a line and a plane 
20110112 

From tom: what are the angles of the diagonal of a rectangular parallelepiped 2in by 3 in by 4 in
makes with the faces...
You know this is a problem that I can't figure out ...I don't know where
the angle and the diagonals where? can you help me with this one? Answered by Penny Nom. 





An air duct in the form of a circular cylinder 
20101219 

From ed: an air duct in the form of a circular cylinder has a cross section if diameter 16 in. the distance between the bases is 20 ft and the elements are inclined at an angle of 50 degrees to the bases. find the amount of magnesia required to protect the duct with magnesia covering 1/2 in thick? tnx Answered by Stephen La Rocque. 





A man made circular lake 
20101125 

From ailish: A man made circular lake has a diameter of 338 m. A bridge is to be constructed across the lake in such a way that it is 119 m away from the center of the lake. How long is the bridge? Answered by Penny Nom. 





A problem that can be solved using trigonometry and geometry 
20101029 

From xolani: In your neighbourhood find a problem that can be solved using trigonometry and geometry. write a report on the problem and how you solved it. the report should contain:
a) a clear description of the problem, accompanied by a diagram and all necessary measurements.
b) a solution to thje problem, showing all calculations.
c) proper theorems and rules must be used as part of the solution. Answered by Robert Dawson. 





Limiting Cases in Geometry 
20100922 

From Niki: Consider a rectangle inscribed in a circle with a radius or R. What are the possible perimeters for the rectangle? Answered by Stephen La Rocque. 





Two perpendicular chords 
20100911 

From edwin: two perpendicular chords AB and CD intersect at P. if X,Y are their midpoints and M the centre of the circle, prove that MP=XY. I do not a have clue on how to do it so can you please help me with it Answered by Robert Dawson. 





Geometry in the Woods 
20100616 

From cleo: what geometric ideas can you find in the woods Answered by Walter Whiteley. 





How far am I from the starting point? 
20100518 

From jilayna: if i walk 5 miles north, 7 miles east, and 3 miles north again.to the nearest tenth of a mile ,how far,in a straight line, am i from my starting point Answered by Penny Nom. 





If (x, 4) is equidistant from (5, 2) and (3, 4), find x. 
20100421 

From abeth: If (x, 4) is equidistant from (5, 2) and (3, 4), find x.
Find the point on the y  axis that is equidistant from (4, 2) and (3, 1). Answered by Penny Nom. 





An irregular octagon 
20100309 

From Gayle: Question from Gayle:
I am building an irregular shaped octagon wooden box.
The measurements are 291/2 inches by 211/2 inches.
Sides are 12 inches.
It will be 36 inches high.
What would the cutting angles degrees be? Answered by Harley Weston. 





Can a line segment curve over two planes? 
20100214 

From Graham: I am working on a math fair project.
Can a line segment curve over two planes?
Such as, if I had a three dimensional L bracket and I drew a line segment
on it with a marker starting on the bottom of the L and had it curve
around the corner and up the top, would it still be considered one line
segment? Or is that two line segments?
Is there a rule that a line segment can only occupy one plane?
Thank you.
Graham Answered by Chris Fisher. 





The volume of a silo 
20100121 

From heather: The height of the silo is 30ft and the face that rests against a barn is 10 ft wide. If the barn if 5 ft from the center of the silo what is the capacity of the silo? Answered by Penny Nom. 





A truncated cone 
20091111 

From Lucian: I need to calculate the bottom inside diameter of a truncated cone.
The top insdie diameter is 1450mm.
The material is 6mm thick
The cone angle is 20 degrees
The slant length is 152mm
I would like a formula so that I can build a spread sheet Answered by Penny Nom. 





A line and a circle 
20091019 

From Renson: Determine whether the line x2y=0 cuts,touches or fail to meet the circle x^2+y^28x+6y15=0.If it touches or cuts ,find the coordinates of the point(s) of contact Answered by Harley Weston. 





Hexadecagon 
20090920 

From Rick: Is there an easy way to figure the even side lengths of a Hexadecagon in layman's
terms, so I know how long to cut the exterior support boards for my pool deck.
The pool is a 16' diameter Hexadecagon and my Wife wants a 4' wide splash deck
all the way around which would make the outside 24' in diameter. Answered by Chris Fisher and Harley Weston. 





Segments of a ring gasket 
20090920 

From Robert: I am in the process of making an Excel spreadsheet in which our sales
team just needs to enter the outside diameter, inside diameter, and
number of segments to price ring gaskets that are too big to fit on a
sheet of material and need to be cut into segments. With your help I
was able to create a spread sheet that can calculate the Chord lengths,
and Segment height on a single gasket segment. I am now stuck trying to
come up with a formula to figure out the height of the second segment
when it is stacked on the first segment, then use it to add more
depending on the quantity of segments needed. I have an illustration
below showing 2 segments (of a gasket that was segmented into 4 pieces)
stacked together. I need to find a formula to get the dimension from
"A" to "B". Answered by Harley Weston. 





Elliptic space 
20090918 

From Htet: What is elliptic space and geometry? Answered by Robert Dawson and Chris Fisher. 





Bisecting rays 
20090909 

From frank: Ray OC bisects angle AOB, ray OD bisects angle AOC, ray OE bisects angle AOD, ray OF bisects angel AOE, and ray OG bisects angle FOC: if angle BOF=120 degrees, then find angle DOE? Confused! Answered by Penny Nom. 





A triangle on a sphere 
20090907 

From Rohit: How do I find the angles of a triangle drawn on a sphere (spherical triangle)? Answered by Chris Fisher. 





A paper towel roll 
20090819 

From Jeff: I am making a spiral tube with paper that is 2" in dia. and 102" long
I will be using paper that is slit 3" wide how many lineal feet of paper will
I need to to cover the 102"
I will be using 3 rolls of paper that will over lap the other by half to make
a hard tube (paper core) in a roll of paper towels
Thanks Jeff Answered by Penny Nom. 





A side of a rectangle 
20090715 

From hanbal: Could please help solving this problem
A(1,3) and D(5,5) are two vertices of a rectangle ABCD. The equation of line AC is 3y=4x + 5
Find
a) the equation of line DC Answered by Chris Fisher. 





liquid in a 3/4 inch pipe 
20090630 

From junior: We are in dilemma at my job. We need to figure out the formula for how much water can our pipe hold. It's inside diameter is 13/16" and is 50ft. long? Answered by Robert Dawson. 





I need help with geometry 
20090506 

From Willena: I have problems in math, but love it all at the same time.
i am currently taking geometry and need help in this area of math as well as
all basics to completely understand the subject in general.
What i would like to know is how can i improve this, very much needed, skill and
as well as understand it? Answered by Robert Dawson. 





A geometry problem 
20090417 

From Yueh: Let ABC be a triangle. Locate the point O inside the triangle ABC such that for points L, M and N lying on its sides AB, BC, and CA respectively, triangles BOL, COM, and AON have the same area, where LO and BC, OM and AC, NO and AB must be parallel respectively. Answered by Chris Fisher. 





Winding paper after a break 
20090410 

From Olen: Question from Olen:
I work in a paper mill and have been handed the task to search for a formula to determine how much paper needs to be added to a parent roll to make up the difference at the winder. (Ex. The spool diameter at the reel is 18.25" we measure roughly 33.5" to make two 58" rolls in the winder. If the is a paper break and the roll diameter in the winder is 30" how much do I add to a single parent roll (22" roughly) to make one 58 " and the 28" needed at the winder. I would appreciate any help to complete this task. I would like to be able to build a chart that operators can refer to based on what is needed. Thank you. Answered by Harley Weston. 





A large, hollow, ice cream cone 
20090403 

From Darah: A manufacturer is making a large, hollow, ice cream cone to serve as an ad for a local BaskinRobbins. The ice cream cone is made up of a cone with height 8 feet, topped by a hemisphere with radius 6 feet. How much ice cream could the hollow object hold? If a gallon is 0.13368 cubic feet, how many gallons does it hold? If 3 gallons of BaskinRobbins heavy cream chocolate blend weighs 24 pounds, how much would the ice cream cone weigh, excluding the weight of the construction material? Answered by Stephen La Rocque. 





Four identical lots 
20090330 

From Marina: I really want to know the answer to this problem for my 6th grade son. I've already sent this question with the drawing but I couldn't send it correctly. I hope this one will pass through.
Q: Divide evenly and identical the figure representing a lot, into four for the 4 siblings. I've sent a figure drawing as attachment. I will describe this in case it will not reach you: its a square divide into 4 triangle and 1 triangle is taken out living a letter M figure and
this letter M figure is the one that will be divided.into 4 even and identical parts.
Marina Answered by Claude Tardif. 





The midpoints of two sides of a triangle 
20090317 

From Manis: Prove that the line joining the midpoint of two sides of a triangle is parallel to the third and half of it. Answered by Robert Dawson. 





A plane cuts a line segment 
20090317 

From Manis: Find the ratio in which the line joining (2,4,16) and (3,5,4) is divided by the plane 2x3y+z+6=0. Answered by Robert Dawson. 





The amount of material remaining on a reel 
20090304 

From James: Question from james:
I am after a standard calculation so that after each usage of the Reel I can get the Remaining Quantity in kilos left on the roll
below is an example of roll
THICKNESS: 30 MICRON
REEL WIDTH: 7.5 CM
REEL DIAMETER: 76 CM
REEL WEIGHT: 7.13 KILOS
The core centre has a 9cm diameter, the weight of the roll is excluding the core , and after each use the diameter of the role is measured.
I am a factory supervisor working on project and need this calculation info for template.. Thanks James Answered by Harley Weston. 





An octagonal landscaping frame 
20090301 

From Richard: Hi
I am trying to put landscape timbers down in octagon shape that measures 6
feet across and outside measures 360 degrees.. The timbers are 4 inches by 4
inches. I need to know at what angle to cut boards and at what length i need to
complete octagon.
Thanking you in advance for your kind assistance.
Richard :) Answered by Harley Weston. 





An octagonal poker table 
20090223 

From Corey: I'd like to build an octagonal poker table using 4'x8' sheets of plywood. I would like each side edge to be approx. 2' wide. I am sure that due to the angles I can do this with one sheet of plywood, but i don't know how to measure for this. Can you help? Answered by Robert Dawson and Harley Weston. 





The floor area in a spherical space station 
20090214 

From Ed: I am writing a science fiction novel that involves a spherical space station with a
radius of 800 meters. Inside, artificial gravity allows parallel floors set 4 meters
apart. If you count the floor that has a radius of 800 meters as Floor 0, then the
next floor up (Floor +1) would by 4 meters above the surface of Floor 0. There
would then be Floor 1 4 meters down from Floor 0. This would continue until
you reach the top or bottom floor, where there is at least 4 meters but less than
8 meters to the top or bottom of the sphere. Obviously the top and bottom
floors would have the (same) smallest area, while Floor 0 would have about 2
million square feet.
My problem is figuring out the total area of all of the floors, or for that
matter, any particular floors or the total number of floors (the total of all the
+ floors, the  floors (these numbers will be the same) plus Floor 0.
Ed Answered by Penny Nom. 





Fertilizer in a bin 
20090203 

From Todd: Hello I am looking for a formula to figure out the fertilizer volume in a hopper bottom bin not only when it is full but part full as well. When you are filling it is heaped up in the middle to make a cone and when you are emptying the bin the cone is inverted so it would be nice to be able to quickly figure out the tonnes partly filled and when full.
Lets say the bin is 32 feet high from top of bin where you fill to the bottom where the product goes out and it is 16 feet in diameter. I know how to calculate the cylinder it is the cones on the top and bottom of the bin I have the main question on. Answered by Harley Weston. 





An octagonal carpet 
20090124 

From Larry: I am cutting a piece of carpet that is 9 feet x 9 feet and need to cut it into an octagon. How far do I cut from the corner of the square. thank you for any help. Answered by Harley Weston. 





A cake must be divided evenly 
20090120 

From kelen: a 10 inch by 10 inch square cake must be divided evenly among 5 people. the top
and all four sides of the cake are frosted. each person must receive the same
amount of cake and the same amount of frosting. there must be no cake left over.
how can this be done? Answered by Robert Dawson. 





Concrete around a pipe 
20090114 

From Doug: How much concrete will i need for a hole that is 20 feet deep 20 inches in
diameter with a 8inch pipe in it. I need to know how much concrete
on the outside of the 8inch pipe. Answered by Penny Nom. 





An area of 64cm squared and a perimeter of 64 cm. 
20090107 

From Dale: i need to draw an object that has an area of 64cm squared and a perimeter of 64 cm. Can you help me out...... Answered by Robert Dawson. 





The volume of a feed hopper 
20081218 

From John: I need to calculate the volume of a feed hopper, and I'm not sure how to break it down. The top of the hopper is 36" x 36", it is 30" deep, and ends at a 6" x 6" plate. One side of the hopper is straight top to bottom, of course tapering on two sides to meet at the plate. The other three sides angle down at about 75 degrees. I need to determine the cubic foot volume of this hopper (it is used for ground coffee) so I can configure a vibrator to knock down residual grounds. Thanks. Answered by Robert Dawson. 





Cubic yards of fill dirt 
20081122 

From Donnie: I need to know the formula to figure cubic yds of fill dirt to fill an area from 4ft. deep to 18 inches deep
this lot is on a slope and I am wanting to level 176 ft long by 4ft. deep
the sides is 115 ft. wide
the upper side is 18 inches deep. Answered by Harley Weston. 





15 cubic yards of dirt 
20081120 

From Phillip: How far, in feet, will 15 cubic yards of dirt cover, if I'm laying it 12 feet wide and 4 inches deep? Please provide formula. Answered by Penny Nom. 





Area of a Decagon 
20081115 

From preethi: what is the formulae of decagon? Answered by Janice Cotcher. 





A barrel on its side 
20081113 

From Dave: Question from Dave:
How many gallons are left in a 36x60 in. barrel (laying on its side) and has 16 in. of gasoline left. I have attached a diagram. Answered by Harley Weston. 





A roll of film 
20081016 

From John: I need to know how to calculate the build up on a roll of film is calculated.
Example: I start with a 6" diameter core, and I start winding .005" thick film on the core, so I am adding a total of .010" to the diameter each wrap.
If I continue to do this for a total length of film of 3000 feet, what will the roll diameter be?
So what I need is the formula to perform this type of calculation.
Can you help me? I want to be able to plug the formula in a spread sheet and to be able to input a core diameter, a film thickness and a total length and get a roll diameter. Answered by Penny Nom. 





Does an oval have sides? 
20081002 

From reid: My 6 yo neice came home with her math homework and she was supposed to identify which objects had sides.One of the objects was an oval.I don't believe it has sides because it is curved and I don't think that would make it an object with sides.What would be the correct answer?Thanks,Reid Answered by Janice Cotcher. 





Constructing An Open Box 
20080723 

From Rita: An open box with a square base is needed to have a volume of 10 cubic feet.
(a) Express the amount A of material used to make such a box
as a function of the length x of a side of the square base.
(b) How much material is needed for a base 1 foot by 1 foot? Answered by Janice Cotcher. 





How many gallons of fuel still in the barrel? 
20080722 

From Charles: I have barrel 6 feet long and 3 feet diameter that is laying on it's side with 5 inches of fuel, how many gallons of fuel still in barrel Answered by Penny Nom. 





A convex quadrilateral in spherical geometry 
20080709 

From Joan: What is the min and max number of obtuse angles possible ia a convex quadrilateral in Spherical Geometry?
I know that the Saccheri has 2 obtuse angles and the Lambert has one, but are there other possibilities?
Thanks for your help. Answered by Chris Fisher. 





I want to fill my backyard slope with fill dirt. 
20080525 

From Piero: I want to fill my backyard slope with fill dirt. The slope is 50 feet wide and the distance from the top of the top of the slope to the bottom is about 15 feet deep and the slope angle is at a 45. I want to know how many yards of dirt do I need to fill a space that is 20 feet out, 15 feet deep at a 45 degree angle. Answered by Stephen La Rocque. 





An octagonal prism 
20080427 

From Melanie: My son is identifying geometric shapes in the real world? We are stuck on octagonal prism, rectangular prism and square prism. Can you help me out with some examples. Thanks Answered by Penny Nom. 





A fish tank in the shape of an irregular pentagon 
20080329 

From richie: i am building a fish tank. it is going to be an irregular pentagon. the sides are going to be
24"
24"
8"
8"
32"(approximately)
there will 3 right angles A, B, E
my question is how to figure out the degree of the angles that are not right angles (C,D)? Answered by Chris Fisher. 





A car tire full of concrete 
20080327 

From robert: I want to build a volleyball net support. I am using a car tire 24"odx16"id filled with concrete. how much will this weigh? thanks Answered by Penny Nom. 





Two circles and a triangle 
20080307 

From Adrian: The vertices of a rightangled triangle are on a circle of radius R and the
sides of the triangle are tangent to another circle of radius r. If the lengths
of the sides about the right angle are 16 and 30, determine the value of
R+r Answered by Penny Nom. 





10 squares drawn one inside another 
20080225 

From Rajesh: There are 10 squares drawn one inside another.The diagonal of the inneremost square is 20 units. if the distance b/w the corresponding corners of any two successive squares is 1 unit, find the diffrence between the areas of the eigth and seventh square counting from the innermost Answered by Stephen La Rocque. 





A real life example of a decagon 
20080212 

From Htet: I have a math dictionary to complete by February 13, 2008, Wednesday, and I need to know what a real life example of a decagon can be. I need help on this! Answered by Penny Nom. 





Three balls packed in a box 
20080207 

From jasmin: Four spherical balls having diameter of 4 cm are placed in a square box whose inside base dimensions are 8 cm. In the space between the first four spherical balls, a fifth spherical ball of the same diameter is placed. How deep must the box be in order that the top will touch the fifth ball? Answered by Stephen La Rocque. 





The interior angles of a parallelogram 
20080128 

From steffie: How do you calculate the interior angle sof a parallelogram? Answered by Penny Nom. 





An irregular octagon 
20071223 

From Sheldon: I am attempting to construct an irregular octagon picture frame out of bamboo. The bamboo is 1" in diameter and the opening should be 20" H X 16"W.
What measurements should be used? Answered by Penny Nom. 





Straight lines 
20071126 

From Divyansh: hello
i am in eleventh class and am, preparing a project on straight lines
i cant really find uses of straight lines and its equations in daily life
i am also thankful to you in advance and am waiting for your answer eagerly because i need to submit my project only this week
thanking you Answered by Penny Nom. 





An isosceles triangle 
20071126 

From Nancy: I needed to help my 9th grade daughter regarding a geometry problem. After a while I realized I am not getting anywhere. I saw that in 2005 someone asked the same question and you gave them a hint. Unfortunately it still did not help. Because I had figured that much!Can you kindly help me proof this problem?
PX and QY are attitudes of acute triangle PQR, and Z is the midpoint of PQ. Can you write a proof that triangle XYZ is isosceles?
I am sure it is something simple I am missing, but I just can not seem to be able to see it. Thank you much. Answered by Harley Weston. 





How many yards of dirt? 
20071116 

From wade: i own 4acres of land and would like to fill it with 10inches of dirt can you tell me how many yard of dirt it will take to do so Answered by Penny Nom. 





A geometric proof 
20071116 

From Julie: Prove that tangents to a circle at the endpoints of a diameter are parallel. State what is given, what is to be proved, and your plan of proof. Then write a twocolumn proof. Answered by Walter Whiteley. 





I need to rebuild a wagon wheel 
20071026 

From Pat: I need to rebuild a wagon wheel, the metal wheel rim is 41" diameter, inside the rim is a one and a half inch by one and a half inch wood wheel.
I thought I would glue up a hexagon from a 2x6 or 2x8 piece of wood and then draw and cut out the 41" diameter wood circle.
? what would work better the 2x6 or the 2x8 and what is the lenghth of the cuts needed in order to give me the 41' diameter I need. Answered by Harley Weston. 





An octagonal table 
20071018 

From Lorne: I am 77 years old and want to build a table top with each side measuring 23 inches.
I believe the diameter would be 55.5 inches. Is this correct and what is the angle of the cuts I have to make? Thank you for your patience. Answered by Penny Nom. 





Four triangles in a square 
20071015 

From Kristina: A square with side lengths of 6 cm is divided into 3 right triangles and a larger isosceles triangle. If the three right triangles have equal area, find the exact area of the isosceles triangle. Answered by Stephen La Rocque. 





The amount of dirt 5 feet deep over a 50 acres 
20071002 

From Debbie: Please tell me how to calculate the amount of dirt stripped 5 feet
deep over a 50 acre site. How do you calculate the amount of dirt in an acre
and then excavating it a certain depth. How does one calculate the amount of
dirt excavated and moved and how to price to charge for the service? Answered by Stephen La Rocque and Victoria West. 





A sector of a circle 
20070926 

From A student: hi im stuck on this question. i have tried to do some, could you please che=
ck it and help me.the answers i have worked out are in red. the question is=
attached. thank you. Answered by Penny Nom. 





An equilateral triangle 
20070913 

From Bibi: An equilateral triangle has a point P inside it. PA, PB, PC are the perpendiculars from point P to the three sides of the triangle. Help me show that PA+PB+PC is the same no matter where the point P is..? Answered by Harley Weston. 





A quadrilateral problem 
20070829 

From James: The sides BC and AD of a quadrilateral ABCD are parallel. X is the midpoint of AB. The area of ABCD is Y. Find the area of the triangle CXD in the terms of Y. Answered by Harley Weston. 





Another circle problem 
20070827 

From Lindsay: Hello. I'm trying to a math problem and have searched the internet for equations, but have come up empty handed. If you could help, that would be greatly appreciated!
The question is stated thus: Find the equation of the following circle:
the circle that passes through the origin and has intercepts equal to 1 and 2 on the x and yaxes respectively. Answered by Stephen La Rocque and Penny Nom. 





Circle Geometry 
20070814 

From Robin: In a triangle ABC, angle A=75 and B=60. A circle circumscribes the triangle. The tangents of the at points A and B meet in a point D outside the circle. Show that ABD is an isosceles triangle with a right angle at D. Diagram included. Answered by Stephen La Rocque. 





Circle Geometry III 
20070717 

From Sean: Two rays are drawn from the same point A outside a circle, and intersect the circle as shown in the picture. Prove that the measure of angle A is onehalf the difference between the measures of arcs BD and CE. Answered by Stephen La Rocque. 





Circle Geometry II 
20070717 

From Sean: Let M be a point outside a circle, and let a line through M be tangent to the circle at point P. Let the line through M and the center of the circle intersect the circle in points Q, R.
Prove that │PM│^{2} = │MQ│ x │MR│ Answered by Stephen La Rocque. 





Circle Geometry  Quadrilateral circumscribing a circle 
20070717 

From Sean: Four lines are tangent to a circle that form a quadrilateral. It appears that the quadrilateral is a trapeziod but this is not a given. Prove that the combined lengths of two opposing sides of the quadrilateral are equal to the combined lengths of the other two opposing sides of the quadrilateral. Answered by Stephen La Rocque. 





Babylonian geometry 
20070617 

From marleen: The following problem and the solution were found on a Babylonian tablet dating from about 2600BC:
Problem:60 is the Circumference, 2 is the perpendicular, find the chord.
Solution:
Thou double 2 and get 4
Take 4 from 20, thou gettest 16
Square 16, thou gettest 256
Take 256 from 400, thou gettest 144
Whence the square root of 144, 12 is the chord.
Such is the procedure. Modern day mathematicians have reasoned that the Babylonian Mathematician who solved this problem assumed that the value of Pi is 3. By explaining in detail how the Babylonian Mathematician must have solved this problem, justify the reasoning of the modern mathematicians. Answered by Stephen La Rocque. 





A geometry problem 
20070614 

From Shamik: ABC is any triangle and D and E are 2 points on AB and AC, respectively. M
is the midpoint of BE and N is the midpoint of CD. Prove that the area of
the triangle (AMN) is 1/4 of that of the quadrilateral(BCED).
Use planegeometry without using coordinates to find the solution. Answered by Shamik Banerjee and Chris Fisher. 





Discovering the incircle of an irregular polygon 
20070525 

From Joaquim: I've been searching in some books and many websites, but I couldn't find a formula or algorithm for discovering the incircle of an irregular polygon, could you please help me? Answered by Walter Whiteley. 





Who was the mathematician that united algebra and geometry? 
20070508 

From Victor: who was the mathematician that united algebra and geometry Answered by Penny Nom. 





Are proofs important in geometry? 
20070507 

From BJ: Are proofs very important to know how to do?
My daughter has been in Geometry & the teacher skipped proofs. Answered by Penny Nom. 





Prove that the triangle ABC is isosceles 
20070305 

From Lisa: I am stuck on this problem... If AB = CD (parellel line), and Answered by Stephen La Rocque and Penny Nom. 





A sphere in a cube 
20061109 

From Lukas: Given a cube and a cross diagonal, what is the largest size sphere that fits in the cube and does not touch or intersect the cross diagonal? Answered by Steve La Rocque, Penny Nom and Walter Whiteley. 





A problem involving a quadrilateral 
20061013 

From Jeff: In the quadrilateral above, AB=AC=AD. If angle BCA = 65, then x=??? Answered by Penny Nom. 





How many line segments are necessary? 
20061004 

From Varun: If you place 35 points on a piece of paper so that no three are collinear, how many line segments are necessary to connect each point to all the others? Answered by Stephen La Rocque. 





An equilateral triangle has been wedged in between two circles. 
20060922 

From Kim:
An equilateral triangle has been wedged in between two circles. How does the diameter of the smaller circle compare to the diameter of the larger circle.
image: circle inside of an equilateral triangle touching all sides of the triangle; both the triangle and the circle inside are placed into a larger circle where the triangle vertices all touch the circle
Answered by Penny Nom. 





An angle in a parallelogram 
20060813 

From Sam: Parallelogram ABCD has diagonal AC equal in length to side AB. CD is produced to E so that D is between E and C. If angle BAC =30 degrees find the size of angle ADE. Answered by Stephen La Rocque. 





A perpendicular intersection of two barrel vaults 
20060721 

From Neal: I'm wanting to build a series of architectural models of different roman and medieval buildings out of cardboard. Once I have perfected the models I want to print them out on card stock so that school kids (or anyone else) can make the buildings.
A feature of many of these models is the cross or groin vault (a perpendicular intersection of two barrel vaults).
A single barrel vault is easy to imagine as a plane (a rectangular piece of cardboard) that will be folded into a semicircular arch.
The intersection of a second barrel vault and this one is presenting me with problems. The second plane needs to have an ellipse cut into it so that when it is folded into the arch, it will mate up with the curve of the first barrel vault.
Given that the two pieces of card have identical widths (and therefore identical arcs in cross section) is there a way to calculate the ellipse that needs to be cut so that it can be cut before the second arch is folded? Answered by Edward Doolittle. 





Calculating the belt length of a three pulley system 
20060716 

From Mark: I have a 3 pulley system with sides abc and pulleys ABC. Pulley A has radius of 10cm, pulley B has radius of 20cm, and pulley C has radius of 3cm. The side lengths are: (center to center of pulleys) between pulleys AB = 75cm, between pulleys BC = 100cm, and between pulleys AC = 50cm. I set these side lengths up as (according to law of sines and cosines) a = 100cm, b = 50cm, and c = 75cm. What is the length of the belt required for this system? I need to know how I would set this problem up and solve. Answered by Stephen La Rocque. 





Geometry proof 
20060423 

From Jade: From a point P outside a circle with centre O, tangents are drawn to meet the circle at A and B.
a) Prove that PO is the right bisector of the chord AB.
b) Prove that Answered by Stephen La Rocque. 





Finding the supplementary angles 
20060422 

From Kendra: Angles ABC and DBA are supplementary. If m Answered by Stephen La Rocque. 





Three circles inside a larger circle 
20060416 

From Meghan: Given three congruent circles tangent to one another (radii = 1), what is the radius of a circle circumscribed around them?
Answered by Stephen La Rocque. 





Two circles 
20060407 

From Louisa: One circle of radius 7cm is touching another circle of radius 4cm. These circles are on a line and the problem is to find the length AB where A is the point marking the bottom of the radius of one circle and B is the point marking the bottom of the radius of the other circle. Answered by Stephen La Rocque. 





A line parallel to a plane 
20060328 

From Ryan:
I was wondering how I would prove the following theorem. I am completely lost at this point and all my other ideas have been extremely complicated and somewhat blurry.
"Through a point outside a given plane, there is at least one line parallel to the given plane."
Answered by Chris Fisher. 





Folding a sheet of paper 
20051215 

From Victoria: The current problem is to take a normal 8 1/2 x 11 sheet of paper, take a corner and fold it to meet the opposite corner, and (without actually measuring) produce a formula to describe the result fold/crease. Answered by Penny Nom. 





A point is twice the distance from y = 5 + 2x as it is from y = 5  2x 
20051209 

From Hazel: A point moves so that its distance from the line y=5+2x is twice its distance from the line y=52x. Find the general form of the equation of its locus. Answered by Penny Nom. 





The length of a chord 
20051103 

From Sue: How do you determine the length of a chord when given the diameter of the circle (1.6m) and that the angle = 7π/8 Answered by Penny Nom. 





A cone with vertex (1,1,2) 
20050926 

From Brandon: Find the equation of a double cone with vertex (1,1,2) and which intersects the xy plane in a circle of radius 4. Answered by Penny Nom. 





Given only the length of an arc & the length of its chord find the radius? 
20050907 

From Robert: Given only the length of an arc (72) & the length of its cord (71), how to find the radius? Answered by Penny Nom. 





The area of a triangle 
20050826 

From Martha: I have a triangle that with a base of 60' and the two sides of 37'. I know the formula for area is A=1/2 (b*h) but how do I find the height??
Answered by Penny Nom. 





Some geometry problems 
20050722 

From Sherry: 1. If Circle K has tangents RT and TY where R and Y are the points of tangency, then angle RKY and angle RTY are supplementary.
2. If one diagonal bisects a pair of opposite angles in a quadrilateral, then the quadrilateral is a kite. Answered by Penny Nom. 





Two tangents to a circle 
20050618 

From Tej: The tangents drawn from points M and N of a circle
having centre O intersect each other at point P. If
angle MPN=60 degrees, NM=10, then find the radius of
the circle and Area of quadrilateral OMPN. Answered by Penny Nom. 





Two problems 
20050429 

From Sara:
#1 A boat is traveling in a straight line across a river from point D, directly opposite town P, to a point Q, two thirds of the distance from town P to town R. Towns P and R are towns on the same side of the lake and are 18 miles apart. Line DQ passes through town S, which is 8 miles north of town R. Points P, Q, and R are collinear. What is the length of QS in Miles?
How many miles does the boat travel across the river?
#2 What is the area of a regular hexagon if the perimeter is 24cm?
Answered by Penny Nom. 





Three tangent circles 
20050125 

From Kate: Two circles, C1 and C2, touch each other externally; and the line l is a common tangent. The line m is parallel to l and touches the two circls C1 and C3. The three circles are mutually tangent. If the radius of C2 is 9 and if the radius of C3 is 4, what is the radius of C1? Answered by Chris Fisher. 





A 6 sided (hexagonal) pyramid 
20050122 

From Steve: im trying to make a 6 sided (hexagon) pyramid, from 6 triangles of 12mm plywood, i know all the angles to cut apart from the one one to join all 6 triangles together. Rough measurements are outer edge (A) of each triangle is 13cm's, length of other 2 sides (B&C) of triangle outside to center is 14cm's with a height of the whole thing together about 6cm's. Answered by Chris Fisher and Harley Weston. 





The area of a triangle 
20050121 

From Amy: In tirangle ABC, AB=6, BC=9, BC is the angle bisector of angle ABC and M is the midpoint of BD. If the area of ABC is 30, what is the area of ABM?
The height comes out greater than the hypotenuse, but the teacher said that there's an answer for it. Can you show me how? Thanks Answered by Chris Fisher. 





Stewart's Theorem 
20050117 

From Amy: In triangle ABC, AB=4, AC=6 and AD=5, where D is the midpoint of BC. Determine BC. Answered by Chris Fisher. 





Arcs and chords 
20050109 

From Aniesha: A chord of a circle is 48 centimeters long and is 10 centimeters from the center of the circle. Find the radius? Answered by Penny Nom. 





A geometry problem 
20050101 

From Alexandra: In triangle ABC, b=40, and angle A= 30 degres. What values of BC will give two solution for angle B? Answered by Penny Nom. 





A geometric proof 
20041211 

From Hanna: Given: ABCD is a quadrilateral;
Prove: ABCD is a parallelogram Answered by Penny Nom. 





Slicing cubes 
20041123 

From Anthony: You are working with a power saw and wish to cut a wooden cube 3inches on aside into 27 1inch cubes. You can do this by making six cuts through the cube keeping the pieces together in the cube shape. Can you reduce the number of necessary cuts by rearranging the pieces after each cut? Answered by Chris Fisher. 





S is between T and V 
20040916 

From Reuben: S is between T and V. R is between S and T. T is between R and Q.
QV=18 QT=6 and TR = RS = SV Make a sketch and answer the following:
Find RS QS TS TV Answered by Penny Nom. 





The railing around a pool 
20040726 

From Bob: I have a 15' circular above ground pool. Around the perimeter of the pool are eleven (11) sections of railing. Each rail has 5 slots at each end for pins. I have calculated that the length of the arc under the railing to be 51.4". what I am trying to determine is the distance between the end points of the arc so that I can figure out which slot to use in the rails without going round and round the pool moving and removing the rails until they finally fit. Been there, done that, no fun. Answered by Penny Nom. 





A proof in geometry 
20040716 

From An: Im taking a geometry course for the summer , and we just started to learn about proofs for about one week. Today in class, we started to do this one proof but didnt finish it because class ended. the problem is as follows. Answered by Penny Nom. 





The center of a circle 
20040526 

From Wan: I am trying to find the radius of an arc. The only things i know about the arc is all referenced from the line of tangency to the arc. on both sides i have a differnt horizontal perpendicular distance to the point of tangency.
left side * right side (*=point of tangency). Then i have 2 difference vertical perpendicular distance of the end points to the line of tangency. I know it sounds very bad in text but this is all i know about the arc. Can you help me find the radius? Answered by Penny Nom. 





The perimeter of a triangle 
20040521 

From A student: In a triangle i have the length of a line and it's opposite angle.how can i calculate perimeter?(the angles are not right) Answered by Penny Nom. 





The height of a triangle 
20040427 

From Danielle: what is the definition of height of a triangle? Answered by Penny Nom. 





Circles in a hexagon 
20040411 

From Crystal: step by step can you show me how to calculate the area of the region inside the hexagon but outside the seven circles. given the radius of each circle is one inch Answered by Penny Nom. 





Trisecting an arbitrary angle 
20040406 

From Joe: Where can I submit my effort on trisecting an arbitrary angle with only a straightedge and a compass? I can do it but I do not have the smarts to prove it.S Answered by Chris Fisher. 





A geometry problem 
20040304 

From Jennifer: I need help with this problem: Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square, and the tangent to the semicircle from C intersects side AD at E. What is the exact length of CE?o Answered by Chris Fisher. 





Napoleon's theorem 
20040227 

From David: How do i prove this : For any triangle, if you make 3 equillateral triangles
using the sides of the the original triangle, the central points of the 3
tringles another triangle that is equillateral.z Answered by Chris Fisher and Penny Nom. 





Is a cylinder a type of prism? 
20040129 

From Rebecca: Is a cylinder a type of prism? Answered by Penny Nom. 





Noneuclidean geometry 
20031208 

From Geoffrey: How can you use noneuclidean geometry to navigate on a sphere? What geometers did work in this area? Answered by Chris Fisher. 





NonEuclidean geometry 
20031203 

From Geoffrey: What are the applications of NonEuclidean geometry (especially hyperbolic and spherical)? Answered by Walter Whiteley. 





A locus 
20031202 

From Tash:
Question:
a)Find the equation of the locus of the point P which moves so that its distance from A(1,2) is always three times its distance from B(5,6)
b) Show that this locus is a circle and states the coordinates of its centre and the length of its radius
Answered by Penny Nom. 





The length of a chord 
20031103 

From David: When Radius=400.00' and Arc=130.58' what is the Cord distance in feet? Answered by Penny Nom. 





Symmetries of a rhombus 
20031102 

From Tonia: why cant an equal sided rhombus have 3 lines of symmetry? you have one line of symmetry on each of the diagonals, and there should be one vertically on an angle. can you please explain the rules of symmetry to me? Answered by Walter Whiteley. 





Two chords 
20031007 

From Lori: Chords AB and CD of circle O intersect at E. If AE=4, AB=5, CE=2, Find ED. Answered by Penny Nom. 





A rectangle in a circle 
20030927 

From Abdu: A rectangle ABCD is inscribed in a circle. If the length of AB is 5 and length of BC is 12, what is the area of circle outside the rectanlge ABCD? Answered by Penny Nom. 





The volume of an earthen pit 
20030912 

From Bruce: This shape would occur at the four corners of a rectangular shaped earthen pit with sloping sides (1:1.5). Depth is 14'. Top dimensions are 170' by 158'. After calculating the easy volume components of this shape, we are left with the end corner pieces. 21' base, 14' height, side hypotenuse 25.24' and corner diagonal 32.83'. We're confused. Thank you for any help you may provide. Answered by Penny Nom. 





Two line segments and a plane 
20030911 

From Laura: Do all figures made up of two segments lie in a plane? Answered by Penny Nom. 





The general equation for a sphere 
20030911 

From Jaidev: Is there any general equation for a sphere? Answered by Penny Nom. 





Can 2 vertical planes intersect? 
20030906 

From Erin: My question is can 2 vertical planes intersect? Answered by Penny Nom. 





A sphere inscribed in a cone 
20030810 

From A student: A sphere with radius 5cm is inscribed in a right circular cone 20 cm in height.find
(a) the base radius ,volume of the cone (b)volume of the shaded space( to 3 sig fig) Answered by Penny Nom. 





A triangle and a circle 
20030321 

From Jynks: We need a formula that we can use to figure this out for work. We aren't math wiz's or students. Basically we know 3 points in space of a triangle, we know the length of each side and the length of the line from apex to base line. Each point of the base line ends upon the circumference of a circle. IS three a way to work out the radius of that circle. Answered by Penny Nom. 





Cutting a board 
20030120 

From George: A person has a sheet of board which he saws into two (2) pieces. The length of the first piece is two thirds the length of the original board, while the length of the second piece is four feet longer than the first piece. How long was the original board? (the length is defined as the longer of the two sides of the board) Answered by Penny Nom. 





The height of a triangle 
20021129 

From Dean: Could you please tell me the formular for me to calculate the height of a triangle. I have the angles and side lengths. I am trying to calculate the height of an isosceles triangle, does this make a difference from a normal triangle or is the formular the same. Answered by Penny Nom. 





Constructing a tangent to two circles 
20021128 

From Tom: I have two circles, different sizes a known distance from each other. We know the radii of the circles. How do I construct a line that is tangent to both circles relative to the segment that connects the centers of both circles? Answered by Chris Fisher and Penny Nom. 





The orthocentre 
20021017 

From Elsie:
 Find the orthocentre of the triangle with vertices at A(3,4), B(10, 3) and C(3,2).
 Find the distance of point X(3,8) from the line that passes through Y(2, 2) and Z (3, 2).
Answered by Chris Fisher. 





A geometry problem 
20020929 

From Sonia: Given ABCD; m a. Find the measures of b. Is there enough information for you to conclude that Answered by Penny Nom. 





A cone that is cut off at the top 
20020923 

From Stuart: I have to work out the dimensions and arcs of a cone that is cut off at the top. I.e Top diameter is 33mm to bottom diameter is 43mm and the depth is 80mm Are you able to work what the flat of this cone would be as I need to design within the flat area and then have it cut out. I really need to know what the flat of it is before it is cut and curled to form the above cone. Answered by Walter Whiteley. 





A Circle is evenly divided into six equal triangles 
20020916 

From Marilynn: A Circle is evenly divided into six equal triangles leaving an area between the outside of the circle and the one side of the triangle. This area is measured as 3.14. What is the length of the radius, one line on the triangle? Answered by Paul Betts. 





An equilateral triangle 
20020611 

From Sarah: Hi. My name is Sarah. I'm a secondary student taking a Math 30C course by correspondence. The question has two parts.
The first part is: Draw an equilateral triangle XYZ. Draw the altitude from X to YZ. Choose any point P inside the triangle or on the triangle. Draw perpendiculars from P to the sides of the triangle. The Second part is:
Measure the altitude h and the 3 perpendiculars s, t, and u to the nearest mm. Repeat as many time as is necessary until you can state a generalization concerning h, s, t, and u. If you could help me, it would be greatly appreciated. Answered by Penny Nom. 





Regular polyhedra 
20020607 

From Sandra: The other day a colleague and I were talking about polyhedra. Is regular a term applied to polyhedra or just polygons? If so, then what would define a regular polyhedron? Would it mean all faces are regular or would it mean that all faces are identical and regular? That is, could a pyramid with equilateral triangles for lateral faces and a square base be considered regular or must the base also be an equilateral triangle? Answered by Chris Fisher. 





Perimeter 
20020605 

From Tava: I'm a grade four student from St. Mary school. In class we've been dicussing perimeters. So this is what we did; First we each got a piece of paper in the shape of the geoboards and our teacher told us to find as many different shapes of area of 12 square units. During this time we were given to find perimeters of shapes that had twelve square units one of our classmates discovered the biggest perimeter possible with twelve square units of 26 units. Another classmate discovered the smallest perimeter of fourteen units. Here's a question: Why are all the shapes with fourteen units all the same shape? and why are all the shapes with twentysix units can be different? After we found the biggest and smallest shapes our teacher told us we each had to find at least one shape of the biggest and smallest. After we each foud a shape with a perimeter of twentysix and fourteen we had to find different shapes with different perimeters. During that time we discovered different perimeters. What we found was fourteen all the way up to twentysix, but they all went by two's. Why didn't they count up by 14, 15, 16, 17, 18 etc? I think it's because the area is an even number. See if you added one "block" or "square" to it you always add three because at least one of the sides is together with another side. Whyare all the perimeters all even numbers? Answered by Penny Nom. 





Overlapping circles 
20020529 

From Naman: There are two circles, big circle with radius R and small one with radius r. They intersect and overlap in such a way that the common area formed is 1/2 pi r^{ 2} (half the area of the small circle) If r=1, find the Radius of the big circle (R)? Answered by Harley Weston. 





3 radians subtends an arc of 27 meters 
20020522 

From Kyle: In circle O, a central angle of 3 radians intercepts an arc of 27 meters. Find the number of meters in the length of the radius. Answered by Penny Nom. 





Bob swam across a river 
20020522 

From Torri: Bob swam across a river 420 ft wide. A strong current carried him 580ft downstream as he swam. Find x, the distance bob actually swam. Answered by Penny Nom. 





Find the angle measures 
20020518 

From Amanda: In triangle ABC; the measure of angle A is 20 degrees more than twice the angle B. The measure of angle C Is five times angle B. Find the angle measures. Answered by Penny Nom. 





Chord length 
20020517 

From Ashlie: How do you find the chord length of one section of a chord if you only have the diameter length and the other whole chord length. WV is the diameter and equals 16. XY is perpendicular to it, and equals 10. They intersect at pt. Z. I need to know what WZ equals. Please help! Answered by Penny Nom. 





Moving a triangle 
20020418 

From A student: find the verticles of a triangle after it is translated 2 units to the left and then is reflected across the graph of y=x+2. The original verticles of the triangle are (2,0), (3,2), and (6,2). Answered by Peny Nom. 





A triangle in a circle of radius 6 
20020326 

From Marko: In a circle of radius 6, a triangle PQR is drawn having QR = 8 and PQ = 10. Determine the length of PR Answered by Chris Fisher. 





A cone in 3 space 
20020320 

From Matthew: Let C in R^{3} be the cone defined by x^{2} + y^{2}  z^{2} = 0 (A) Let P be the plane described by x + 2z = 1 (i) Find a description of P in terms of two parameters s and t . . . Answered by Walter Whiteley. 





A circular wading pool 
20020304 

From Patrick: The community of melfort is planning to build a circular wading pool in the park. The pool will cover an area of 1000m^{2}. The building committee has decided to put a 5m cement pad around it. How much additional area will the cement pad take up? Answered by Harley Weston. 





Two circles inscribed in a rectangle 
20020227 

From Amina: Given a rectangle with dimensions L=6, H=5. Two circles are inscribed such that they touch each other(circles are adjacent to each other) and also their circumferences touch 2 sides of the rectangle. One of the circles has radius=4. Find the radius of the other circle. Answered by Penny Nom. 





An octagonshaped deck 
20020220 

From An instructor: How can you solve for finding the side measurements of an octagonshaped deck that is 10 feet long and 10 feet wide. Answered by Penny Nom. 





Nets for pyramids 
20020214 

From Michelle: I want to have my students create nets for pyramids and I need to know how to find the correct range of degrees for the interior congruent angles of the isosceles triangular faces. For example, I know for a squarebased pyramid that 77 degrees will work; however, I know other angle measures will also work. I'm just not sure how to find the minimum degree measure to have the net actually "work". I'm assuming the maximum would be 89 degrees, although that would make for a very tall pyramid. Answered by Penny Nom. 





Normal lines 
20011211 

From Kristie: Why are perpendicular lines called normal lines? Answered by Chris Fisher. 





The "pi" of a circle in hyperbolic space 
20011119 

From Alex: How can you find the "pi" of a circle in hyperbolic space (or is it the same). I would like to know because our environment is hyperbolic and if the "pi" of hyperbolic space is irrational, it would follow that space is non discrete. I would greatly appreciate any help in this question. Answered by Walter Whiteley. 





A circle and a triangle 
20011109 

From Tasha: I have a circle that has an equalateral triangle inscribed in it. The tip of the triangle (B) is at the center of the circle with the other corners (A & C) extending to the sides of the circle. I need to know the equation to find the linear length of AC. I also need to find the cordial length of the circle from point C to A. Answered by Penny Nom. 





Applied geometry 
20011102 

From Jenny: Where can I find some handson activities for my Applied Geometry classes? I want to do more activities with them that allow us to get out of the classroom. However, I want to use activities that use only inexpensive equipment because I usually buy the equipment myself. Answered by Walter Whiteley. 





Where is the fourth point? 
20011024 

From Mike: Four points are placed at random on a piece of paper. Connect the three points of the triangle of the largest area. What is the possibility that the fourth point is in the triangle? Answered by Penny Nom. 





The average of two polygons 
20011023 

From Irene: How can I prove that the average of two polygons will give me another one? Answered by Walter Whiteley. 





The amount of gravel needed to fill a hole 
20011006 

From Rhett: My name is Rhett and my problem is...I am a contractor and I am having problems determining the amount of gravel(in tonnage) needed to fill this hole,the measurements are 60' in length,22' in width,and 14' in height....the problem is that it is not a usual box shaped hole or in this case a rectangle shaped hole,but more of a triangular shaped hole.I refer to the triangular shape as the interior shape of the crater not the exterior,which is shaped like the above dimensions.If you could help it would be greatly appreciated.P.s.This was a retaining wall project,built by myself, in front of a sloped end of a yard,so if you could imagine a 14" high hill with a landslide looking face,then build in your mind a three sided rectangle in front of it using the hill side that slopes as the fourth side of the rectangle,then you may be able to imagine what I mean as a triangular shaped interior of the hole. Answered by Penny Nom. 





A circle and a triangle 
20011004 

From Christina: The points (3,4), (9.2), and (3,2) define a circle and a triangle.  find the areas of the circle and the triangle. Find the difference between their areas.
 Find the length of a side of a square with the same area as the triangle.
 Find the length of a side of a Square with the same are as the circle.
Answered by Penny Nom. 





The median of a trapezoid 
20011001 

From Laura: Given: A (1,2) B (9,2) C (7,2) D (3,4) Find the endpoints of the median. Use exact values. Write the equation using the letters from the given trapezoid. Verify the theorem using algebra. Answered by Penny Nom. 





Counterclockwise 
20010914 

From Rolanda: When Descartes invented the coordinate system he decided to number them counterclockwise. Why? Answered by Chris Fisher. 





Similar triangles 
20010908 

From Dave: I am standing on the bank of a river ( whose banks are parallel here) directly opposite a boathouse, B, on the opposite bank. I walk along the bank of the river past a signpost, S, until I reach a point C distant 60 metres from where I started walking. I then walk away from the bank, at right angles to the bank, until I reach a shady tree at D. Attached to teh tree is a sign stating that this spot is 45 metres from the signpost. C is 36 metres beyond S and B and S are in line from D. (a) How far did I walk away from the bank of the river?? (b) Calculate the width of the river? Answered by Penny Nom. 





Intersection of perpendicular cylindrical surfaces 
20010731 

From Charlie: Please consider two right circular cylinders, perpendicular one to the other, and of unlike radii in a 3 dimensional Cartesian space with mutually perpendicular x,y,z axes. If one cylinder is centered on the y axis with radius ra, and the other on the z axis with radius rb, then the expression for the first surface would be x^{2} + z^{2} = ra^{2}, y = any number. Likewise, the second cylinder's surface would be x^{2} + y^{2} = rb^{2}, z = any number. It is my intent to define the curve at the intersection of these two cylindrical surfaces. From sketching the conditions it appears that this intersection resembles an ellipse folded about its minor axis. Answered by Chris Fisher. 





Radian measure 
20010726 

From Amy: i have to find out what is meant by the radian measure of an angle and compare it to the measure of an angle in degrees. Answered by Harley Weston. 





Three chords 
20010628 

From Paul: AE is a diameter of a circle and AC, CD and DE are chords of lengths 1, 2 and 3 respectively. (See the diagram.) Find the ridius of the circle. Answered by Harley Weston. 





Three tangents to a circle 
20010627 

From Stephanie: The three lines PS, PT, and RQ are tangents to the circle. The points S, X, and T are the three points of tangency. Prove that the perimeter of triangle PQR is equal to 2PT. Answered by Chris Fisher. 





A three legged stool 
20010627 

From Teri: I wanted to know why a three legged stool is always steady, and why a four legged stool is not. I am wanting to know the mathematical reasoning behind this. Answered by Walter Whiteley. 





Geometry problems involving triangles 
20010607 

From Sandi: Find the radius of the largest circle contained in a right triangle whose legs are 8 and 15 and hypotenuse is 17. If the right triangle has legs a and b and hypotenuse c, find an expression for the radius of the circle. Answered by Penny Nom. 





Geometry 
20010421 

From Rebecca: How do you prove the following: Let CD be an altitude of triangle ABC and assume that angle C=90 degrees. Let r1 and r2 be the inradii of triangle CAD and CBD, respectively, and show that r+r1+r2=CD, where r is the inradius of triangle ABC. Answered by Chris Fisher. 





Pyramids 
20010418 

From Kelly: I'm in tenth grade and I know that there's some formula for finding out the slope of the side of a pyramid. I thought it could be the pythagorean therom, but I'm not sure if this works. Please send me the formula as soon as possible, I need it for a project. Answered by Penny Nom. 





A geometry proof 
20010418 

From Melissa: Extend the bisectors of angle A, angle B, and angle C of triangle ABC to meet the circumcircle at points X, Y, and Z respectively. Show that I is the orthocenter of triangle XYZ. Answered by Chris Fisher. 





Isoscles and scalene 
20010417 

From Autumn: explain where the term isoscles and scalene came from? Answered by Chris Fisher. 





The sides of an octagon 
20010413 

From Craig: How do I figure the length of the sides of an octagon when all I know is the diameter (4.375). Answered by Penny Nom. 





An elliptic tunnel 
20010324 

From Janna: A tunnel is built under a river for a road 12m wide with a 2m sidewalk on either side. The top of the tunnel is semielliptical. A local bylaw stipulates that there must be a clearance of at least 3.6m at all points on the road. If the smallest possible ellipse is used, find the clearance at the center of the road. Answered by Harley Weston. 





Two locus problems 
20010308 

From Janna: A point P moves such that it is always equidistant from the point G(2,5) and the line defined by y=3. Find the equation of the locus. I got as far as the equation: 3y^{2} 4y = x^{2} + 4x  16 and didn't know what to do from there. Of, course that whole equation could be wrong. Question 2: P is always twice as far from A(8,0) as it is from B(2,0). Find the equation of the locus. Once again, I got as far as y^{2} = x^{2} 8x 56, and got stuck. Answered by Harley Weston. 





MIRA 
20010227 

From Constantinos: What is a "mira," and how is it used in terms of topology (in geometry)? If you can answer my question, and even refer me to online or other resources to find out more, I would greatly appreciate it. Answered by Walter Whiteley. 





Mr. Moser's roof 
20010221 

From Michelle: Mr. Moser is planning to replace the roof of his home. He needs to order a pack of shingles. Each pack covers 100 sq. ft. of roof. Without a ladder, Mr. Moser can not climb to the roof to measure it. Instead, he measures his attic and finds it to be 40 ft. long, 24 ft. wide, and 5 ft. high at the peak of the roof which is in the center of the house. Although the roof is even with the side walls, he estimates the roof line continues 1.5 ft. beyond the front and back walls. How many full packs of shingles should Mr. Moser order to cover his roof? Answered by Penny Nom. 





Congruence and symmetry 
20010221 

From Chris: My name is Chris and I am a secondgrade teacher. I would like to know what the difference is between congruent and symmetry, and how do I explain this to my class? I know that congruent means the same, and symmetry is two identical sides. Is there a difference between the two? I know there must be, but I don't know what or how to explain these two terms. Answered by Walter Whiteley. 





Faces 
20010221 

From Sandy: How many faces are there on a sphere? What are the faces of a cone? What is the definition of a "face" of a 3D object? Answered by Walter Whiteley. 





Symmetry 
20010215 

From Sonam: What is symmetry? Who invented symmetry? what are the different kinds of symmetry? Answered by Penny Nom. 





An irregular polygon 
20010209 

From Jason: I have a 5 sided irregular polygon I am trying to figure out the area of. There are no right angles in the polygon as far as I can tell. I do not know any angles. Answered by Chris Fisher. 





Partitioning of an arbitrary line segment 
20010208 

From David: Did Euclid's Geometry include a construction for the regular partitioning of an arbitrary line segment? Answered by Chris Fisher. 





Building a circular silo 
20010124 

From Natasha: We wish to build a circular silo with internal diameter 10 feet. How much concrete will we need to pour the foundation, if we only need a 1 foot wide and 1 foot deep ring on which the silo walls will sit? Assume the 4 inch thick silo wall rests on the middle of the ring. Answered by Penny Nom. 





A prism 
20010118 

From Nigel Ayling: What is the mathematical definition of a prism, I am confused by the following definitions as they appear to be contradicto... Answered by Walter Whiteley. 





A quartercircle and two semicircles 
20001231 

From Christopher: Inside the quartercircle are two semicircles with the same radius, (r). Which has a greater area, G or L? Answered by Penny Nom. 





A Trapezium problem 
20001215 

From Ben: A trapezium has a perimeter of 22cm. The 2 parallel sides are such that the length of one is three times the length of the other. The nonparallel sides are equal. If the distance between the parallel sides is 4cm, find the lengths of the 4 sides. Answered by Claude Tardif. 





Networks of satellites and linear spaces 
20001208 

From David: Let us suppose some companies have collaborated to place several satellites in orbit. Let us call the set of all satellites that a given company helped place in orbit a network. Finally let us assume the following 4 rules.  There are at least two distinct satellites.
 For each pair of satellites there is exactly one network containing them.
 Each network contains at least two distinct satellites.
 For each network, there is a satellite not in it.
What is the least number of satellites. what is the least number of networks? Answered by Penny Nom. 





Optical illusions 
20001206 

From Jessica: Hi, my name is Jessica, 7th grade, and Im doing a Math Fair project on optical illusions. As one of the required factors, we need a "mathmatical significance" paragraph. Unfortunatley, I can only think of one way that optical illusions have to do with math, and thats time because some optical illusions tell you to look at the picture for a certain amount of time. Answered by Penny Nom. 





A point that a group of lines pass through 
20001205 

From Ross: A point that a group of lines pass through is called a________? Answered by Chris Fisher. 





The aspect ratio of a rectangle 
20001204 

From Ron Delavigne: The aspect ratio of this rectangle is 4:3. That is A to B is 3. And B to C is 4. If I know the lenght of A to C is 19 inches, how can I find the length of A to B, and B to C. Answered by Penny Nom. 





A piecewise linear equation 
20001124 

From Jacky: There is a light bulb and it is given that the light bulb cost $0.75 and the cost of operating it is $0.0081 per hour. From the information give, I came up with the linear equation: Let c be total cost and Let h be hours used. Therefore: c = 0.0081h + 0.75 represents the total cost of the light bulb and the electricity. However, the second part of the question added the fact that the light bulb will only last for 800 hours. If the light bulb is replaced as soon as it burns out exactly after every 800 hours, how can I write an equation that represents that? Is it possible? What would it look like on the graph. Answered by Harley Weston. 





What are adjacent angles that equal 360 called? 
20001122 

From David: I know that supplementary angles add to 180 degrees and that commplementary angles add up to be 90 degrees, but what are adjacent angles that equal 360 degrees called? Answered by Chris Fisher. 





Find the 3D angle 
20001118 

From Jacky: Included is the diagram. I am trying to find out the angle of ABC. Is it possible? How? Answered by Penny Nom. 





Inscribing a circle in a rhombus 
20001116 

From Jacky: A rhombus ABCD is drawn in which the diagonals are 12 and 20 units long. A circle is inscribed in the quadrilateral with the centre of the circle right on the intersection point of the 2 diagonals. The circumference of the circle touches all 4 sides of the rhombus. Is it possible to find the radius of the inscribed circle? If so, how and what is it? Answered by Chris Fisher. 





Expanding a garden 
20001116 

From Janeth Rojas: Mr Jones's garden has an area of 21 squares meters. He wants to increase its size by 1/2. Draw a picture to show what his new garden might look like. Be sure to give the new area and demensions, and show your reasoning. Answered by Penny Nom. 





Crown molding mitre cuts 
20001106 

From Jim Tomfohrde: My question has to do with making mitre cuts when installing crown molding. Crown molding is the trim that is put up at the top of walls with one edge on the wall and the other edge on the ceiling. To make a mitre cut on your mitre saw for a 90degree corner you can lay the molding flat on the saw base, set the bevel of the blade to 34 degrees and the mitre to 31.5 degrees (these may be slightly appoximate). Of course depending on which piece of molding you're cutting you will cut one end or the other, or use the left or right end. These angles allow the cuts to line up and form a seamless corner when they're put in place on the wall/ceiling at 90 degrees. My question is this  is there some mathematical formula from which the 34 degrees and 31.5 degrees are derived. I want to know this because in many cases the corner is not 90 degrees but can be more or less, and in these instances I would like to know if I can calculate the bevel and mitre to use based on the angle of the corner. Answered by Harley Weston. 





A chord length 
20001017 

From Al Paas: How to determine the length of a chord given the diameter of the circle and the maximum distance from the chord to The circle? Answered by Chris Fisher. 





The sum of the cubes is the square of the sum 
20001010 

From Otoniel: Without using mathematical induction, or any other method discovered after 1010 a.d. , prove that the sum of i^{3}, (where i, is the index of summation) from one to, n, is equal to ((n*(n+1))/2)^{2} Answered by Penny Nom. 





Tessellations 
20000917 

From Lindsay: What is the word that means a shape repeated over and over again to make something like a quilt pattern? Note: I'm pretty sure it is either a fractal or tesselation. Could it be that the pattern itself is a fractal but the entire quilt would be a tesselation? Answered by Chris Fisher. 





Two geometry problems 
20000909 

From Becky: What are all the real values of x that are solutions for the inequality [x2] < 6? ( it's less than or equal to) What is the distance between the points with (x,y) coordinates (3,2) and (3,1)? Answered by Peny Nom. 





How many planes contain a line and a point? 
20000830 

From Harold: How many planes contain each line and point? Answered by Harley Weston. 





Three points on a line 
20000825 

From Casey: I am trying to find the slope and yintercept of an equation. I have THREE x values and THREE y values. How do you do it? Help! Answered by Penny Nom. 





The angle of rotation 
20000803 

From Jay: I have the following information Given. (X1, Y1) Origional Point (X2, Y2) Origional Point After a Rotation (Xa, Xb) Center of Rotation What formula would I use to figure out the angle the point was rotated? Answered by Chris Fisher and Harley Weston. 





Area of a circle 
20000803 

From Larry: I know the formula is pi r squared. For a circle 4 inches in diameter, do I multiply pi (3.1416) by the radius (2") then square the answer to that ie: 3.1416 X 2 squared or do I square the radius (2 X 2") then multiply by pi (3.1416) ?? Answered by Penny Nom. 





Graphing an inequality 
20000802 

From Lori: How do I find x and y and graph this problem 3x + y < 5 Answered by Penny Nom. 





Making a paper cone 
20000730 

From John: The question of how to lay out & cut out of paper, cones came up. I would like the cone have : A base of 4 inches and height of 4 inches, 6 inches, 8 inches. Answered by Harley Weston. 





The circumference of a circle 
20000730 

From Not a student: An equalateral triangle is enclosed in a circle. The three corners touch the edges of the circle. One side of the triangle is 12. What is the circumference of the circle? Answered by Penny Nom. 





A semicircle and a triangle 
20000728 

From Ben: A semicircle and an isosceles triangle ABC have the same base AB and the same area. The equal angles in the triangle are BAC and CAB. I have to find the value of each of these angles. Answered by Harley Weston. 





Parallel tangents 
20000630 

From Ebony Indalecio: I need to prove the theroem: Tangents to a circle at the end points of a diameter are parallel. Answered by Walter Whiteley. 





Tiling a floor 
20000627 

From Carolyn Clarkston: A square tile measures 6 inches by 6 inches. What is the least number of tiles needed to cover a rectangular floor area of 9 feet by 12 feet? Answered by Walter Whiteley. 





Projecting a line segment onto a plane 
20000608 

From Monica: What is the measure of the angle determined by a 14 inch segment and its projection into a plane if the length,in inches, of the projection into the plane is 7 inches? Answered by Penny Nom. 





Surface area of a contact lens 
20000606 

From Evie Contreras: I would like to know how to calculate the surface area of a contact lens with a radius of 7mm? I know that the area of a circle is pi R squared, but a contact lens has a dome. Answered by Harley Weston. 





A centroid problem 
20000602 

From Kerstin: An isoceles triangle has sides measuring 13 cm, 13 cm, and 10 cm. Find the distance from the centroid to the vertex of a base angle. Answered by Harley Weston. 





Adjacent Angles 
20000521 

From Katherine Keys: Can a straight angle be an adjacent angle to another angle? Answered by Chris Fisher. 





Volume of a sphere 
20000521 

From Kevin Partridge: Does anyone have a way to physically demonstrate how to explain the volume formula for a sphere? Or perhaps how to derive the formula without calculus? Answered by Harley Weston. 





A conic in standard form 
20000518 

From Tara McConkey: Im havign trouble converting the following conic to standard form, i know that the conic is a hyperbola but that is all 16x^{2}9y^{2}160x18y+247=0 Answered by Harley Weston. 





Graphing a linear function 
20000517 

From Chelsea: I need help with grahing linear functions.If you could email me back the basics and how tos I would be much appriciative. Answered by Penny Nom. 





Reflection off a sphere 
20000512 

From Mark Adami: Given two points P,E and a sphere. Find a point on the sphere, T, so that a line from P that bounces off the sphere at T goes through point E. Answered by Chris Fisher and Harley Weston. 





Supplementary angles 
20000509 

From Suzanne: We know that: Supplementary angles are two angles whose sum equals 180 degrees and complementary angles are two angles whose sum equals 90 degrees. Are supplementary and complementary angles necessarily adjacent? or can they be nonadjacent? Answered by Chris Fisher. 





Parallel and perpendicular lines 
20000508 

From Jimmy Lumpkins: Need a method for solving the following problem: Find the equation of a line through point P that is parallel or perpendicular to another line. Answered by Paul Betts. 





Area of an ellipse 
20000502 

From Kaushal Shah: How do I Calculate the area of a ellipse known the length of any related thing. Example, suppose if I know the length of latus rectum, major&minor axis etc. Answered by Walter Whiteley. 





Fractals 
20000429 

From Rachel Maginn: What are Fractals? I am doing a research project. Any information would be great. I need to know the history behind fractals, and how they are used. I would like some examples like the snowflake and a fractal tree. Any other examples would be appriciated greatly. Answered by Harley Weston. 





Monica's geometry problem 
20000427 

From Monica: Given: ABCD is a square; AX is perpendicular to BY Prove: Angle 1 is congruent to Angle 3 Answered by Chris Fisher. 





Side length of an octagon 
20000422 

From Unknown: If I have an octagon that is 12 feet across (side to opposite side) how can I find the length of the sides? Answered by Harley Weston. 





Circumference = Area 
20000419 

From Scot George: The area and circumference of a circle has the same measurement. Find the radius. Answered by Chris Fisher. 





Uniting algebra and geometry 
20000416 

From Beth: Who is the mathmatician that united algebra and geometry??? Answered by Claude Tardif. 





White and blue paint 
20000409 

From Lauren Emerson: A truck full of cans of blue and white paint flips over on the road. There are dots of blue and white paint everywhere. Prove that two dots of the same color paint are exactly pi feet apart. Answered by Penny Nom. 





Surface area of a cylinder 
20000407 

From Jim Campbell: I am going to cover the outside of a shaft with some material. How do I figure the square inches of the outside surface of the shaft? Shaft is 6" in diameter and 24" long Answered by Harley Weston. 





Lining a cone 
20000406 

From Jim Campbell: I am not a student, I am trying to solve a business problem. The question. If I want to put a lining in a chute that is cone shaped, how do I calculate the size steel plate I need to do that. The cone is 10' in diameter at the top and has a 20" hole at the bottom. The total height of the chute is 8'. Answered by Harley Weston. 





The side length ratios of some triangles 
20000404 

From Alexis Lockwood: I am doing a project for my Math 30B class regarding the side length ratios of 454590 degree and 306090 degree triangles. I would really appreciate any assistance in answering the following questions, or even direction to an appropriate web site or resource on the matter. Answered by Harley Weston. 





Why a Right angle? 
20000403 

From Joseph Mizerek: I was wondering why a 90 degree angle is called a Right angle. I mean why isn't called a left angle. Answered by Haragauri Gupta. 





Sylvester's Problem 
20000323 

From Sheryl Webb: I am trying to find a proof of the theorem: Given n points in a plane, there is a line that contains exactly two points. Answered by Chris Fisher. 





Surface area of a sphere 
20000322 

From Gina Wilkie: How can I demonstrate to my middle school students the reason for the formula for the surface area of a sphere? Answered by Walter Whiteley and Chris Fisher. 





Four questions 
20000317 

From Ibrahim Bin kasmin:
 What is a hexahedron?(please show a picture of a hexahedron).
 How do we make a cube out of three pyramids?(show me the picture).
 How do we find the approximate perimeter and area of a hibiscus leaf?
 What is a Pascal triangle?
Answered by Penny Nom. 





Putting in a pool 
20000316 

From Katie: If your digging a hole for a pool and the pool is: Length= 11m Width= 6m Sallow Depth= 1.1m graduating to 'Deep' Depth= 1.8m What is the volume of soil that will be taken out? And if a bobcat can excavate and remove 10m3 (qubed) of soil an hour how long will it take him to excavate the soil. Answered by Penny Nom. 





Geometrical solids 
20000315 

From Sarah:
 What geometrical solid has 8 edges and 5 vertices?
 What geometrical solid has 12 edges that are all the same length?
Answered by Walter Whiteley. 





An equilateral triangle in a circle 
20000311 

From Michael Setlik: An equilateral triangle is drawn within a circle such that all three points of the triangle just touch the inside of the circle. Given the diameter of the cicle as six inches what is the length of the sides of the triangle? Answered by Harley Weston. 





Congruent parts of congruent figures 
20000310 

From Erica: Yesterday, I recieved a test problem asking to prove two line segments equal. Here is the problem as I was given it: Given: paralleogram ABCD AE is perpendicular to DB CF is perpendicular to DB Prove: AE is equal to CF I answered the problem as follows: . . . Answered by Walter Whiteley. 





Grazing area for a goat 
20000310 

From Amy: A goat is tied in the middle of a side of a square building whose sides are 2 yards long. The rope is 4 yards long. What is the grazing area for the goat? Answered by Harley Weston. 





Proportionality in a triangle 
20000301 

From Courtney Smith: I would appreciate assistance with the following problem In triangle ABC,segment MN divides sides(segment)AC and (segment)AB proportionally. If the coordinates are A(3,7),M(0,10) and N(8,22) and if AM:MC = 3:1, find the coordinates of B and C. Answered by Penny Nom. 





Folding a page 
20000301 

From Krista Bischoff: One corner of a page of width a is folded over and just reaches the opposite side. Express L, the length of the crease, in terms of x and a. I can't get the picture to copy to this form so I guess I will have to try and describe the picture the best that I can. The top right hand corner is folded to the left side, almost half way down. The width of the paper is a ( the width of the bottom part which is not folded.) The creased side is L and the part shorter part of the folded area is x (the part that would have been the top right of the original piece.) Answered by Chris Fisher. 





Midpoints and endpoints 
20000215 

From Jessica Sipes: I need to know how to find and endpoint using the midpoint and the other endpoint. Answered by Penny Nom. 





Is a square a rectangle? 
20000215 

From Jaireh: This is something that aroused a debate in class: A rectangle was defined as a parallelogram with 4 right angles. A square was defined as a parallelogram with 4 congruent sides and 4 right angles. I need written and conclusive proof that some rectangles can or cannot be squares. I tried insisting that some of them can.. but without proof nobody will listen. Answered by Walter Whiteley. 





Filbert Family Circus 
20000204 

From Sarah: As Clyde moves his broom around the circus ring, he thinks that he has finally found a job where he can make a clean sweep of things. Clyde is sweeping the ring where the lions perform in the Filbert Family Circus. The ring is 76 feet across and Clyde is using a broom 3 feet wide. He starts at the outside edge and works his way to the middle, making circles around the ring. After sweeping 3/4 of the ring, Clyde sees the lions coming with their trainer and scurries out of the ring. How many trips around the ring did he make? Answered by Penny Nom. 





Euclidean Math puzzle 
20000124 

From Margaret Matthews:
(Check out this website: Simeon's Triangle Puzzle ) I have tried to figure out how this could be, because everything I know about it tells me it can't be. However, I can't seem to make it NOT work. Two right angle triangles. They are each cut up into four identical pieces. In the first, all the pieces fit together so that there are NO empty spaces; in the second, presumed to be identical in size to the first, the pieces are slightly rearranged, and now, there IS a space in the triangle. Answered by Patrick Maidorn and Claude Tardif. 





Arclength of a circle 
20000119 

From Holly: What is the formoula for finding the arc length of a central angle of a circle?? Answered by Harley Weston. 





Pyramids and prisms 
20000118 

From Tyler: What's the definition of a Triangular Prism and a Triangular pyramid. Answered by Penny Nom. 





Taxicab geometry 
20000116 

From Jack: Im doing an investigation entitled 'taxicab geometry', ive attempted it and have done most of the practical part of it. But i cant seem to see the equation behind it all. please guide me in the right direction. They provide a regular grid with regular horizontal and vertical lines. The lines are roads and the actual squares are blocks of hoouses/ buildings. In taxicab geometry the distance between place A & B is worked out by adding together the horizontal and vertical distances. each square is counted as i unit. Part 1 (I've done this) A taxix cab firm is based at A. the posistion B is 7 units away from A. investigate all the posistions of B at 7 units. investigate for different distances. . . . Answered by Penny Nom. 





A roll of paper 
20000115 

From Richard: I have a roll of paper, wrapped around a corrugate core, whos diameter is 10.750 in. The outer diameter of the roll is approx. 60 in. The thickness of the paper is .014 in. I am trying to find out how much linear feet of paper is left on the roll, given only the diameter of paper remaining on the core. Answered by Chris Fisher and Harley Weston. 





Parallel planes 
20000110 

From Hugo Alvarez: When two parallel planes are cut by a third plane, the lines of the intersection are? Answered by Claude Tardif. 





Rectangular hyperbola 
19991215 

From Aarti Chand: Why do they call a rectangular hyperbola, rectangular and where the normal hyperbola looks like a rectangle and the rectangular hyperbola looks like a sqaure? Answered by Chris Fisher. 





A model area 
19991215 

From John Ost: Hello, I am a college student taking an elementary math course I need if possible assistance to developing an area model 36 x 25 that shows each of the four separate partial products. I must know how to do the computation 36x25 showing each of the four partial products separately, and indicate how each corresponds to the drawing that is required of the area model. Answered by Penny Nom. 





Cutting a carpet 
19991215 

From Heather: A rectanglular piece of carpeting is 90 inches long and 90 inches wide. How can the carpet be cut into two pieces of equal sides and shape to cover an area of 100inches? There can only be one cut and no scraps. Please show me how. Answered by Penny Nom. 





A goofy clock 
19991120 

From Kate: While repairing a watch, a jeweler removed the hands and inadvertently replaced the hour hand on the min. spindle and vice versa. he set the hands to read 2:00pm, which was the correct local time when I picked up the watch. A few minutes later, I noticed that the hands were taking goofy positions. What was the first time thereafter that the watch would show the correct local time? Answered by Chris Fisher. 





Isosceles triangles 
19991012 

From Amber: In defining the types of triangles, our class was stumped by a question asked by one of the student. Maybe you could help. The definition of an equilateral triangle is a triangle with three congruent sides. The definiton of an isosceles triangle is a triangle with at LEAST two congruent sides. The question is, if an isosceles triangle only requires at Least two of the sides to be congruent, could an equilateral triangle be called an isosceles triangle? Answered by Penny Nom, Walter Whiteley and Chris Fisher. 





The circumference of a circle 
19991005 

From Mara Frost: what is the formula to find the circumference of a circle, or if there is no formula, how do you find the circumference of a circle? Answered by Penny Nom. 





Regular and irregular shapes 
19991003 

From Samuel Tighe: What is the difference between a regular shape and an irregular shape? Are a rectangle and a triangle regular or irregular shapes? Answered by Walter Whiteley. 





Intercepts 
19990924 

From Cassandra: My book says to find where the X and Y intercept, i dont understand who to do this problem. Can you please help here is the problem. it didnt quite explain the instructions. Answered by Penny Nom. 





Surface area of a cone 
19990918 

From Frothy: I don't understand how to find the surface area of a cone. The height is 12cm and the radius is 5cm. Answered by Walter Whiteley. 





Rolling Circles 
19990912 

From Craig Ellis: We have a circle of radius 3. inside the circle and tangent to the circle of radius 3 at one point is a circleof radius 1. The question is if we could roll the smaller circle around the inside of the larger circle how many revolutions would it take to get around to where we started. Answered by Chris Fisher and Walter Whiteley. 





The three jugs problem 
19990902 

From Kent Lane: I wonder if you could help me figure out this secondary Discrete Math Problem. I cannot figure out where this comes from. Here's the question: You have three containers. Container 1 is a three (3) liter container. Container 2 is a five (5) liter container. Container 3 is an eight (8) liter container that is full of liquid. The goal is to get 4 liters in one of the containers. Stipulations: There are no marks on the containers to measure out the liquid. All you know is that 1 is 3 l., 2 is 5 l., and 3 is 8 l. full of liquid. Answered by Chris Fisher. 





Why is slope designated m? 
19990818 

From Peter Komlos: Why is the slope of a line is designated by the letter "m"? Answered by Penny Nom. 





Geometry 
19990729 

From Jessica: How do you even do Geometry. Like what do you need to learn first and like a step by step plan.I realy need help I need it before school starts PLEASE!!!!!!!!! Answered by Walter Whiteley. 





How to carpet a room 
19990531 

From Appleby: A room which is 9X12 is to be covered with carpet but the carpet has been provided in one 8X1 piece and one 10X10 piece. The larger piece is to be cut into two pieces so that the room can be covered in carpet. Answered by Stacey Wagner. 





Girth 
19990526 

From Carolyn Bulkley: I am trying to explain to my son (who is in the 8th grade) how to figure girth. I'm afraid I have just confused him. Is there a simply formula to figure the girth of a box. for example: I have a box that is 27" L X 22" W X 21" H. Answered by Penny Nom. 





Shapepreserving transformations 
19990504 

From J McAndrew: A shape preserves its shape if a rotation, translation or scaling is performed on it. Are these the only continuous transformations which have this property? These transformations if performed on the parts and then summed have the same effect as the transformation being applied to the whole; are these linear transformations? Who, and what area of mathematics has classified all transformations of this type completely? Answered by Chris Fisher. 





Parabolic shapes 
19990504 

From Justin Ailor: Can you give me some parabolic shapes? Answered by Penny Nom. 





A rhombicosidecahedron 
19990430 

From Himmat: What is a rhombicosidecahedron? Answered by Harley Weston. 





An equilateral triangle on a square 
19990426 

From Ed: My Grade 8 class and I were discussing the solution to the following problem: What is the area of the largest equilateral triangle that can be drawn on a 5 cm square. We used 5 cm as the base of our triangle and then drew the other two legs of 5 cm each to make the equilateral triangle. We then drew an altitude from the upper vertex to the base of the triangle. Using the law of Pythagoras with side a of 2.5 and side c of 5 we calculated side b to be 4.3 cm (the altitude). Therefore the area of the triangle would be 5 x 4.3 divided by 2 or 10.75 square cm. The answer key to this resource says I am wrong. What do you think? Have we interpreted the question incorrectly? Answered by Chris Fisher and Harley Weston. 





A ladder problem 
19990422 

From Michael Blade: There is a cube box 3feet x 3feet x 3ft resting against a vertical wall on level ground. Resting against the outside corner of the box is a ladder 10 feet tall, this ladder is of course resting on the ground but also against the outside corner of the box and rests on the wall. The question the ladder is divided into two unequal section bounded by the box to the ground and the box to the wall. what are those dimensions? Answered by Penny Nom. 





Circles 
19990421 

From Alex Elkins: How do you find the circumference of a circle if you only know the radius and the square feet or inches of the circle if the radius is 18 inches, If done in inches do you multiply by 12 to get the square feet? Answered by Jack Lesage and Harley Weston. 





Volume of oil in a tank 
19990417 

From Lars Waldemarsson: My problem is to get an equation for the depth of the oil in a gastank formed like a cylinder. The cylinder is in a horizontal position and by a stick you will be able to get the depth of the oil in the tank. All I need is an exmaple which I can build on. By this equation you will be able to get the volume of the oil if you know the depth. Answered by Harley Weston. 





Dividing a Circle 
19990412 

From Mike Kenedy: I am having trouble with a homework question for bonus marks. A Circle is continually divided by lines that do not intersect the center so that they produce the most pieces of circle. For example  1 line divides the circle into 2.
 2 into 4.
 3, however into 7.
 4 into11
 5 into 16
 6 into 22
 7 into 29
 8 into 37
 etc...
I am stumped and cannot figure out the equation, though I'm sure it involves squares. Can you help? Answered by Penny Nom. 





Rhomboid 
19990325 

From Monica Armour: I need to see a net of a rhomboid. Where can I find one on the net? Is it like a square paramid with the top chopped off? Help! This has me stumped. Answered by Jack LeSage. 





NonEuclidean Geometry 
19990210 

From Robert Smith: Is noneuclidean geometry necessary for the college bound student? I have students that are inerested in teaching math one day. My school is restricted to Euclidean Geometry. Answered by Walter Whiteley and Jack LeSage. 





Lunes 
19990204 

From Kai G. Gauer: A prof once told me that a certain type of lune is quadrable given that the diameter is an integer. She used the construction of a right isosceles triangle within a semicircle and later constructed another semicircle on the base of the first semicircle and used area subtraction to show equality to a smaller triangle with quadrable area. What happens when the original inscribed triangle is no longer isosceles? She mentioned something about other lunes also being quadrable; but not all. What are the dimensions of other such lunes? Note: I'm not certain if I still have my hercules account; please simply post on Q&Q. Thanks! Answered by Chris Fisher. 





Patterns 
19990107 

From Melis Kalay: I'm confused about questions like these: 1. 2by2by2 cube: If this cube was painted blue on the outside,  how many cubes would have 3 blue faces
 2 blue faces
 1 blue face
 0 blue faces
Answered by Jack LeSage and Penny Nom. 





Geometry patterns lesson plans 
19981231 

From Vicki: hi,,, my name is Vicki and I am a new 5th grade teacher.... Anyway, I'm supposed to come up with a lesson plan to  Explore patterns that result from cominations of "reflections, rotations, and translations of geometric figures.
The plan is to include:  writing/metacognition, assessment strategies, interdisciplanary connections, supplemental materials, or textbook, and Bloom's taxonomy level.
Any help you could give would be greatly appreciated. Thanks Answered by Jack LeSage. 





Intersection of planes 
19981122 

From Dave Rasmussen: I am a teacher of secondary mathematics with a question about the uses of Three Dimensional Coordinate Geometry. I have been teaching my students to write equations of planes and lines,  to find the intersection of these and the distance between them. What I am having difficulty finding are good applications of these techniques to "real world" situations. Can anybody help me? Answered by Walter Whiteley and Harley Weston. 





A tetrahedron inscribed in a cube 
19981118 

From Jane: In analyzing a cube, I would like to find a tetrahedron inscribed in the cube which has none of its faces in the planes of the faces of the cube. I would like to see this tetrahedron outlined in the cube. My name is Jane and my email address is BARSOIAN. I am an elementary education student. Answered by Walter Whiteley. 





Two sides and a bisectrix. 
19981111 

From Victor Grinshtein: I am looking for someone who can tell me how to construct a triangle by 2 sides and a bisectrix using a compass and a ruler. Answered by Chris Fisher. 





Area of a Triangle. 
19980305 

From Amanda: How do you figure out the area of a triangle? You already have the perimeter and height Answered by Penny Nom. 





Two Inscribed Trapezoids 
19980127 

From James: A hexagon inscribed in a circle has three consecutive sides each of length 3 and three consecutive sides each of length 5. The chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 3 and the other with three sides each of length 5, has length equal to m/n, where m and n are relatively prime positive integers. Find m+n. Answered by Haragauri Gupta. 





Shimin's Geometry Problem 
19971202 

From Ong Shimin: ABCD is a rectangle. X and Y are the midpoints of BC and CD respectively. W is a point on AB such that AW : WB = 2 : 1. Z is a point on AD such that AZ : ZD = 2 : 1. WY intersects XZ at O. If the area of triangle WOZ is 84 centimeters squared, find the area of triangle XOY. Answered by Chris Fisher. 





A geometry problem 
19971120 

From Herman: When produced, two equal chords AB and CD of a circle meet at P in an angle of 24 degrees. If H is the midpoint of AB and K is the midpoint of CD, calculate the size of angle HKD. Answered by Penny Nom. 





How many intersections? 
19971008 

From James: (a) A collection of eight points, no three collinear. If lines are drawn between each pair of these points, how many points of intersection would there be? (b) what would your answer have been in part (a) if there had been n points to start with? Answered by Chris Fisher. 





The Length of a Chord. 
19970726 

From Nathan Arthur: Picture a 9 inch diameter circle. Inside that circle is a 6 inch diameter circle tangent to it. Then, tangent to both circles is a 3 inch diameter circle. So there are three circles, two smaller ones inside a big one, all of them just touching but not overlapping. Now picture a chord on the 9 inch circle that is created by making a line that is tangent to both the 6 and the 3 inch circles and extending it to the edge of the 9 inch circle. I need the length of that cord. Answered by Chris Fisher. 





A Geometry Problem 
19970409 

From Gina M. Pisco and Rebecca Henry: Three segments of 3, 4, and 5 inches long, one from each vertex of an equilateral triangle, meet at an interior point P. How long is the side of the triangle? Answered by Richard McIntosh. 





The Real Pythagoras 
19970316 

From Michael Gaskin: I am wondering if you have any information about Pythagoras and his accounts in math. Answered by Chris Fisher. 





Three Spheres 
19970114 

From Alan Schnerch: Three spheres of diameter 2 are placed on a level surface so that each sphere touches the other two. A fourth sphere, also of diameter 2, is placed on top of the other three so that it touches all of the other spheres. The distance from the level surface to the highest point of the top sphere is . . .. Answered by Chris Fisher and Harley Weston. 





Magic Square 
19951020 

From Marianne and Carrie: How can an 8 by 8 square have the same area as a 5 by 13 rectangle? Answered by Denis Hanson. 





Point de partage 
20000221 

From Sebastian Murciano: J'aurais besoin de savoir où je peux trouver de l'informations, ou estce que vous pouvez me donner de l'information sur : Point de partage d'un segment étudié en Secondaire 4. Answered by Claude Tardif. 





Maths 
19990111 

From Stephane Roissard: Soit ABC un triangle dans lequel les trois médianes sont de meme longueur. Montrer que ce triangle est quilatéral. Answered by Jack LeSage. 

