







An arch in the form of a semiellipse 
20200420 

From Anggelica: an arch in the form of a semiellipse is 8 feet wide at the base and has a height of 4ft. how wide is the arch 1foot above the base? Answered by Penny Nom. 





A parabolic arch 
20200206 

From icyy: how high is the parabolic arch of span 20 feet and height of 16 feet, at a distance 5 feet from the center?
what equation will I be going to use? thank you Answered by Penny Nom. 





The length of an arc 
20190428 

From Patrick: If an arch is 48 inches wide at the base and 30 inches tall at its apex, what is the length of the arch? Answered by Penny Nom. 





An arched window 
20170724 

From Gerry: Looking to make a full size template for an arched window. Need increments every 16". The radius is 138' 0 9/16" , the chord is 226" and the rise at center of chord is 43" Answered by Penny Nom. 





A parabolic arch 
20170105 

From Rand: It is most likely already been answered but I can not seem to find the right key words for the search engine?.
What I am looking for is, if you have an have arch/arc and you know the degree of slope and the height of the arch/arc from ground lvl; how do you factor the decreasing angle/#’s to get the distance tween the two feet on the assumption that the arch/arc is curved all the way to ground lvl?
a. where the legs widen continuously (till they hit ground) so yes parabolic &
b. where the legs come down straight after a ½ circumference run.
What I am focusing is the parabolic.
Many Thanks Answered by Harley Weston. 





A search area 
20160813 

From tammy: if your searching an area and you go 300 km from point A and search 380° what or how much area would you search? Answered by Penny Nom. 





Heights at various points along an arc 
20160415 

From Isiah: So I am working on a problem with a few friends; you have an arc with the center of its chord at 0,0. We also have a known sagitta and a known radius of curvature.
How do we calculate the height extending in both the positive and negative directions?
Central sag: 2.48
Chord length: 9.6 Answered by Penny Nom. 





Shooting a ball at a target 
20160216 

From Thys: Hi
I have a problem with the formula that i use .(for programming)
I have looked all over the web to find a solution but no luck.
I have a cannon that shoots a ball at a target
I use this formula to calculate what my initial velocity must be to hit the target
at a angle of 30 degrees and a distance of 15m (the cannon and target position is known)
It works perfectly if both is at same height but if one is higher or lower it miss.
In an example I am working with the range is 30m, the angle is 45 degrees and the target is 10m higher than my position.
Please help
Formula = V0 = √RG / Sin(2α) Answered by Harley Weston. 





A parabolic arch 
20151130 

From Muhammad: An arch over a road has a parabolic shape it is 6 meter wide at the base and is just
tall enough to allow a truck 5 meter high and 4 meter wide to pass
a):
assuming that the arch has an equation of the form y=a(x)^2+b use the given
information to find a & b. explain why this assumption is reasonable.
b):
sketch the graph of arch equation Answered by Penny Nom. 





Archimedes, Euclid and "Circular Reasoning" 
20151115 

From Ron: I have read about Archimedes and his work with sphere in cylinder and cone in cylinder and the volume relationships. Did he or any others also extend this to regular based polygon based regular like pillars, and columns? The ratio of 1/3 to 1 whole holds true with all regular based columns as example: a regular pyramid having a regular hexagon base inside a regular hexagon column of equal height. Answered by Chris Fisher. 





The distance over a Quonset 
20150820 

From jane: total base of hemisphere is 30 ft
apex height is 20 feet
what is total length over dome Answered by Penny Nom. 





Archimedes Burning Mirror 
20120717 

From Frakeetta: Archimedes Burning Mirror
There is a story about Archimedes that he used a “burning mirror” in the shape of a paraboloid of revolution to set fire to enemy ships in the harbor. What would be the equation of the parabola that one would rotate to form the appropriate paraboloid if it were to be designed to set fire to a ship 100m from the mirror? How large would the burning mirror need to be? What is the likelihood that this story is true? Answered by Robert Dawson. 





A parabolic arch 
20120104 

From Swathi: A plan for an arch in the shape of a parabola is drawn on a grid with a scale of 1m per square.
The base of the arch is located at the points (0,0) and (15,0). The maximum height of the arch
is 18m.
a)Determine the quadratic function that models that arch
b)State the domain and range of the function Answered by Penny Nom. 





How much work is done? 
20111015 

From Jean: "A conical buoy that weighs B pounds floats upright in water with its
vertex "a" feet below the surface. A crane on a dock lifts the buoy
until its vertex just clears the surface. How much work is done ?" Answered by Penny Nom. 





Find the rate at which the searchlight rotates 
20110417 

From Meredith: A searchlight is position 10 meters from a sidewalk. A person is walking along the sidewalk at a constant speed of 2 meters per second. The searchlight rotates so that it shines on the person. Find the rate at which the searchlight rotates when the person is 25 meters from the searchlight. Answered by Penny Nom. 





Will the ball clear the tree? 
20101114 

From MK: Sam hits a golf ball with a fiveiron a distance of 120m horizontally. A tree 45m high and 35m in front of Sam is directly in the path of the ball. Will the ball clear the tree if the ball makes a parabolic curve and has a maximum height or 80m? Answered by Brennan Yaremko. 





Body measurements 
20100406 

From Amirul: Recently I'm proposing my research question to my teacher for my extended essay. I'm an IB student.
My research question is regarding the estimation of human in buying trousers through reference of neck. What does the relation between the diameter of the neck and the diameter of the waist?
I want to see how far does the estimation theory is true for different type of people with different BMI(body mass index)..
But teacher said that it is golden ratio...so nothing interesting... =(
really??? But i search on net.... state that my idea seems do not have any relation with the golden ratio so far..... i just want ask you... am I able to perform in my extended essay if i continue with this research question?? Answered by Robert Dawson. 





The height of an arch 
20100102 

From kamer: given the radius 1.696 also the cord length 1.958 find the height between the cord and the arch. Answered by Penny Nom. 





The layout of an arch 
20090818 

From Steven: I am trying to layout a large radius between 2 points in a building and
need a formula to figure different senarios for example:
radius is 187'6"
distance between 2 points is 34'8"
need points 16" apart along the line between the 2 points to create the
radius
please help Answered by Stephen La Rocque. 





An arched or round top window 
20090407 

From Dale: I need a formula to figure the lineal footage of trim require to trim an arched or round top window. The variables that I have consist of the width of the window the height of the arc and the radius. Answered by Harley Weston. 





The height of an arc at the peak 
20090401 

From Ed: What is the term used to describe the height of an arc at the peak? Answered by Stephen La Rocque. 





A parabolic arch 
20090328 

From Jeni: A doorway is in the shape of a parabolic arch.
Find the width of the doorway 1m above the floor.
Given: the height and the width of the doorway is 4m and 3m respectively. Answered by Penny Nom. 





Archimedes' formula for parabolic arches 
20090123 

From La: Use calculus to verify Archimedes' formula for y=9x^2. Prove Archimedes' formula for a general parabolic arch. Answered by Harley Weston. 





An arch is in the form of a semi ellipse 
20081103 

From jessica: An arch in the form of a semi ellipse has a span of 10 meters and a
central height of 4 m. Find the heights of the arch at a point of 3 meters from the semi minor axis. Answered by Penny Nom. 





A bridge is built in the shape of a parabolic arch 
20080602 

From megan: A bridge is built in the shape of a parbolic arch. The bridge has a span of 192 feet and a maximum height of 30 feet. Find the height of the arch at 20 feet from its center. I need the equation and what to fill into the equation...please and thankyou! Answered by Penny Nom. 





The length of an arc 
20080516 

From Don: I am trying to determine the length of an arch with a two foot backset from 32 foot frontage. Answered by Harley Weston. 





A parabolic arch 
20080214 

From Angela: A parabolic arch has an equation of x^2 + 20y  400 = 0 where x is measured in feet. How do I find the maximum height of the arch? Answered by Penny Nom. 





A large concrete shape 
20080116 

From Keith: what is the cubic yards of an area that is not a perfect 1/4 circle?
The dimensions are 100ft. x 60ft. x 125ft. curcumferal arch x 3ft. depth? Answered by Stephen La Rocque. 





An arched entry 
20071128 

From amber: i am working with an arched entry. i know that the radius is 25' and the height is 20'11". i need to know the length of the arch and degree of bend of the arch. how do i find these? Answered by Stephen La Rocque. 





The radius of an arch 
20071110 

From Mark: How do you determine the raduis or diameter of a circle based on the folowing information:
1. The distance along the circle between two points is 35'2". This creates an arch.
2. The (chord) distance between the two points is 30'8".
3. The distance from the center of the chord (on a 90 degree) to the arch is 6'10 3/4". Answered by Harley Weston. 





Completing the square 
20071101 

From Mark: An architect is designing a museum entranceway in the shape of a parabolic arch represented by the equation y = x2 + 20x, where 0 x 20 and all dimensions are expressed in feet. Determine the maximum height, in feet, of the arch. Answered by Stephen La Rocque. 





parabolic arch 
20071024 

From ABHILASH: How find parabolic arch perimeter. Answered by Harley Weston. 





Parabolic arch 
20071009 

From Nisa: A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose suitable rectangular coordinate axes and find the equation of the parabola.
Then calculate the height of the arch at points 10 feet,20feet,and 40 feet from the center. Answered by Stephen La Rocque. 





The perimeter of a regular polygon 
20070918 

From Ashwynn: why does the area of regular polygons with a perimeter of 1000m increase as the number of sides increase? 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 steel arc 
20070531 

From Huw: Two gate posts 48cm apart and a perfect arc of steel is to be made joining the two posts on top. this steel arc is to measure 12cm higher than the top of the gate posts in its centre point.
the question similar to this was asked by "daryl" and answered by "Penny"
If you could reply to this i would be very grateful. Answered by Penny Nom. 





A cabinet with an arched front 
20070409 

From Joe: I am building an arched front cabinet that is 71 inches wide, 12 inches deep at both ends
and 16 inches deep at the center. To accurately build this cabinet I need to known the radius of
the circle that would form that arch.
Thanks,
Joe Answered by Penny Nom. 





An arched opening for a large doorway 
20070408 

From Richard: I am trying to build an arched opening for a large doorway...I know the vertical sides of the opening to be 8'9" from the floor to the lowest point of the arch on each side...I know it is 15 1/2" from the center horizontal point to the top of the arc...I know the vertical sides are 11'11" apart...what I need to know is the radius to create the proper arc. Can you help? Answered by Stephen La Rocque. 





A parabolic arch 
20070329 

From A student: I am trying to figure out how to work this problem as it doesn't have many
details.
The problem ask for an equation to satisfy a parabolic arch y = 16  0.25x^2
for y>=0.
Find the width w of the arch. Answered by Stephen La Rocque. 





The width of an arch 
20070328 

From Brad: A parabolic arch satisfies the equation y= 16  0.25x^2 for y >= 0. Find the width w of the arch. Answered by Penny Nom. 





A roadway over a river 
20070312 

From Taranjeet: My teacher has given us bridge with only one measurement. From the river to the roadway is 50 metres in length (vertically) The question he wants us to find out is. What is the distance between the vertical supports. He has said that: At a horizontal distance of 'x' metres from the foot of the arch the height of the arch, the height of the arch above the river 'h' metres is given by: h=1/40(x squared) = 3x I don't understand how to find the distance between the support beams. Thank you Answered by Penny Nom. 





Can the trailer safely pass under the bridge? 
20070102 

From Jim: A truck hauling a doublewide trailer needs to pass under a parabolicarched bridge en route or take a 50 mile detour. The trailer is 14 feet high and 15 feet wide. The arch supporting the bridge at this underpass is 18 feet high at the center and 40 feet wide at the base. Can the trailer safely pass under the bridge? Answered by Stephen La Rocque. 





Splitting A Circle Evenly 
20061220 

From Joe: I'm trying to make a game board and instead of having it square, I would like to give it a curve (the game is Parcheesi). The attached diagram is pretty much completed (done in AutoCAD). What I would like to know is how to manually find the points that intersect the red line. In other words, evenly split the semicircle into 8 pieces. Answered by Penny Nom. 





The radius of an arch 
20061115 

From Kelly: I am trying to achieve an arc height of .375 on the length of 17.375. Answered by Penny Nom. 





A fountain of water jets forms parabolic arches 
20060503 

From Jennifer: Let's say in you have a fountain and the water jets form parabolic arches. The center of the fountain, being the origin of the coordinate system, it is elevated 5 feet off the ground, . The equation formed the water arch is y= x^{2}+4x, what is the radius of the basin needed to catch the water at ground level? Answered by Stephen La Rocque. 





A parabolic arch 
20060502 

From Mike: A bridge over a river is supported by a parabolic arch...arch is 200 m wide at water level...the maximum height of the arch is 80 m..what is the height of the arch measured from a point on the water 40m from the center of the arch? Answered by Stephen La Rocque. 





Framing an arched wall 
20050812 

From Mike: I'm framing a building wall with a curved (arcing) top section. The radius of the section is 74'6" with a height above finish floor of 16'0". The horizontal run of the arced section is 23' 1 1/2" with a low height above finish floor of 12'4". If I start with a 16' stud at the high end how long are the subsequent studs if they are on 16" centers? Short of laying this out on a tennis court how can I work out the lengths of the studs? Answered by Penny Nom. 





The volume of a sphere. Why 4/3? 
20050530 

From Lauren: You know when you find the volume of sphere? I know the formula is V= 4/3 pi r^{3} but why do they use 4/3? Answered by Penny Nom. 





Marching legion 
20040424 

From Art: A column of soldiers is 100 meters long. Their sargeant at the rear of the column gives the order to march. The sargeant marches alongside the column to its head and then back to the rear, at which point he gives the order to halt. In all, the column of soldiers has marched 100 meters. How far has the sargeant marched? I say 187.5 meters, but those who teach or who have taught mathematics tell me no. Some say much more and some different. What do you say? Answered by Penny Nom. 





A parabolic arch 
20040119 

From Teresa and Robyn: A bridge over a river is supported by a parabolic arch...arch is 200 m wide at water level...the maximum height of the arch is 80 m..what is the height of the arch measured from a point on the water 40m from the centre of the arch Answered by Penny Nom. 





x^{ 4} + x^{ 5} = 100 
20021027 

From Bill: One of my students has stumped me. He asked how to solve the equation 4^{ x} + 5^{ x} = 100 All I can think of are graphing methods to get an approximate solution. What am I missing? Answered by Harley Weston. 





Bridges and parabolas 
20001118 

From Lauren: My name is Lauren, and Im a secondary school student in Ontario. For my gr11 advanced math class I have to find out how and why parabolics are used in arch bridges and write 3 paragraphs on it. People who cohse satelites and whatnot are lucky  I've found a ton of info, but for arch bridges there seems to be nothing. Answered by Harley Weston. 





Cairo tesselation and Archimedean duals 
20000621 

From Joyce DuVall: I am looking for a picture of the Cairo tesselation, and pictures of the Archimedean duals. Do you know of any good web sites or books? Answered by Penny Nom. 





Calculus Research Questions 
20000522 

From William Wright: I am a Calculus Teacher, and me and my class ran into these two problems without solutions in my manual, we got answers, but are unable to check them. If anyone gets this email and can respond to this with the solutions it be greatly appreciated. . . . Answered by Harley Weston. 





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 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. 





Linear programming and optimization 
19990409 

From Shams: What is Linear programming and optimization? Answered by Jack LeSage and Penny Nom. 





Operations Research 
19981008 

From Lisa Barrett: What is the history of operations research and the study of linear programming? Answered by Judi McDonald. 





Approximating pi. 
19961104 

From Ben Dixon: How do you calculate Pi? Do you have to somehow combine the equation for a circle with the formula for the circumference? Answered by Chris Fisher. 





Solides d’Archimède 
20140429 

From Clémentine: Pourquoi une pyramide a base carrée n'est elle pas un polyèdre archimedien ?
J'ai pourtant essayé d'en construire un avec tout ses cotés égaux et ça fonctionne !
Aidez moi je n'en dors plus la nuit ? :S Answered by Chris Fisher. 





Le salinon d'Archimèdre 
19990311 

From Don Craig: I am trying to find the English translation of "Le salinon d'Archimèdre" and would appreciate any help. This is a figure, presumably studied by Archimedes, created from 4 semicircles. Since I can't draw it for you, I will try to describe it with the help of the 5 collinear, horizontal points below. . . . . . A B C D E A semicircle is constructed on AE as diameter (let's say above AE). Two more semicircles are then constructed with diameters AB and DE on the same side of the line AE as the first semicircle (above it). Finally, a fourth semicircle is constructed on diameter BD, this time on the opposite side of the line AE from the others (i.e. below the line). These semicircles and the region enclosed by them constitute what is called in French "Le salinon d'Archimèdre". If you know the English name of this curve I would appreciate it if you let me know. Answered by Harley Weston. 

