







How long will it take to dig the trench? 
20200506 

From Marielena: If the production rate for hand digging a trench is 1.2 mh/cy, how long would it take for one man to dig a trench 2 feet deep by 1 foot wide by 216 feet long? Answered by Penny Nom. 





A kinky curve 
20161006 

From tammie: Koch’s kinky curve is created by starting with a straight segment and replacing it with four segments, each 1/3 as long as the original segment. So, at the second stage the curve has three bends. At the next stage, each segment is replaced by four segments, and so on. How many bends does the curve have at the third stage? Answered by Penny Nom. 





Can you construct a regular 21gon? 
20160308 

From Peter: hi, i know that if i use a compass to draw a circle, i can use the same setting to mark 6 intervals along the circle circumference, how would i go about marking out 21 equally spaced points around the circumference?
if there an online calculator i can us, or some other interesting trick?
tia
peter Answered by Robert Dawson. 





Constructing a cone 
20150312 

From Levi: While the mathematics at the welding shop page was very helpful there is one vital part missing. If I have never built a cone how do I figure out how much bigger the diameter of my
circle has to be when laying flat on the floor verses the diameter when it has been pulled into a cone. Answered by Harley Weston. 





Constructing a triangle 
20130822 

From Nazrul: The base, the difference of the angles adjoining the base and the sum of the other
two sides are given. How can I draw the triangle?
Please help me. Answered by Chris Fisher. 





A triangle construction 
20130727 

From Nazrul: Two angles and the difference of the lengths of their opposite sides of a
triangle are given. How can I draw the triangle.
Please help me. Answered by Chris Fisher. 





Drawing an isosceles triangle 
20120510 

From Nazrul: How can I draw an isosceles triangle whose each angle adjacent to the base is twice the vertex angle? Answered by Chris Fisher. 





Gravel, sand, cement and an equilateral triangle 
20120321 

From saheed: how many tonnes of gravel and sand,bags of cements will be required to concrete 5feet depth/deep of 4feet equilateral triangle? Answered by Harley Weston. 





Making a truncated cone 
20110218 

From lisa: We need to make a cone that has the following dimensions.
143/8" diameter on large end
133/8" diameter on small end
4" tall
What are the dimensions I need to cut in order to make a cone with one seam? Answered by Stephen La Rocque. 





Forming a square 
20091021 

From christianah: Two parallel lines have the equations y=x+4 and y=x2.Two additional lines are drawn to form a square.What is the side length of the square?Write possible equations for the additional lines.Explain and justify your reasoning. Answered by Penny Nom. 





Making a cone 
20090819 

From angela: how can i make a cone with a 6cm of heigth and has 2cm radius in the opening?? Answered by Stephen La Rocque. 





Constructing an isosceles triangle 
20090727 

From Sanjay: How to construct an isosceles triangle ABC with a base BC = 5.4 centimetre and altitude AD = 4.7 centimetre? Please help. Answered by Janice Cotcher. 





Draw an octagon with an area of 18 square centimeters 
20081202 

From Heidi: Draw an octagon with an area of 18 square centimeters Answered by Penny. 





A geometric construction 
20081017 

From M: Given any 3 parallel lines on a plane, how to construct an equilateral triangle with each vertex on each line? Answered by Chris Fisher. 





A parallel line to a given line 
20080412 

From john: A parallel line to a given line through a given point not on the a given line Answered by Harley Weston. 





Constructing the centre of a circle 
20071106 

From Carolyn: I have a line segment AB. I need to divide a segment into 3 parts that are congruent. Please help how to divide it. The answer that I was given previous was not the way the teacher wanted it.
I also need information on how to find the center of a circle given an arc. Answered by Penny Nom. 





Dividing a segment into 3 congruent parts 
20071030 

From Carolyn: I am doing construction. I have a line segment drawn. I need to divide a segment into 3 congruent part. How do I do that? Answered by Penny Nom. 





An equilateral triangle with height 2 inches 
20071023 

From Christine: I'm doing an project in school about tessellations.
But first, I have to construct an equilateral triangle with an altitude of exactly 2 inches.
I know how to draw an equilateral triangle...but I don't know what I have to do in order for the triangle to have an altitude of 2 inches. Answered by Penny Nom. 





Vehicle collision 
20070731 

From Tania: If a driver falls asleep at the wheel of a newer model car and slams into
the rear of a parked classic mustang (28603280lb) and the parked car
is thrown 100 ft across the street, what would be the minimum speed
required by the newer car in order to move the mustang? Answered by Penny Nom. 





Constructing an octagonal deck around a circular pool 
20070420 

From Cliff: [I am building an] octagonal desk encompassing 17 foot diameter circle for pool.
I have seen other octagonal calculations but none of these tell me how much allowance for a circle to fit within the octagon without losing the circle edge can anyone help
thanks cliff Answered by Stephen La Rocque. 





A truncated cone 
20060528 

From Phil: Hi, I am an art student and I am trying to make a "truncated cone" (ie: a cone with the top cut off) out of sheet metal. I need to design a template first and am having problems working out the angles. The truncated cone is 250mm high, 550mm wide at the bottom and 290mm wide at the top. Can you help? Answered by Stephen La Rocque. 





A truncated cone 
20051203 

From Sonny: I need to create a template for a cone that has a 2" opening at the top, a
4" base and stands 6" tall. Can you tell me how to achieve this? Answered by Penny Nom. 





A slump cone 
20051027 

From Wendy: we are trying to make a slump cone (used to measure the slump in concrete). It has dimensions of 8" diameter on the bottom, 4" diameter hole on the top and a height of 12".
Please help, it is getting frustrating. Answered by Penny Nom. 





A conical hat 
20051022 

From Manish: I need to make a conical hat for my daughter's upcoming fancy dress, the circumference of the base(hollow) is 50 cms,the height of the cone is 30 cms,what should be the dimensions of the paper which will make a cone of the beforementioned dimensions? Answered by Penny Nom. 





Constructing a quadrilateral 
20051007 

From Jayasri:
Can we construct a unique quadrilateral with the following information:
The lenghts of all the sides of a quadrilateral are known.
The angle between one of the sides and the Xaxis is known.
Answered by Chris Fisher. 





Constructing figures 
20050920 

From Kim: I would like to know how to draw different shapes:
Regular Octagon with sides of length, 1 unit
Equilateral Triangles, with sides of length 1 unit
Regular Hexagons, with sides of length 1 unit
Isoseles Triangles, with hypotenuse of length 1 unit
Answered by Penny Nom. 





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. 





Two matrix problems 
20050330 

From Sue: Question 1
Suppose all matrices in the equation below are square and invertible. Solve for x .
BA1XB1 + 2BA + In = 0 (the symbol "0" here denotes the matrix of all 0's in it)
Also, A1 or B1 is indicating inverse and "In" = for example, A1 times A
I hope you understand the above. I have to show all the steps.
Question 2
Suppose we consider the set of all 2x2 matrices along with the operations of matrix addition and multiplication. Do they form a field? Why or why not?
I think the answer is no because under multiplication it is not commutative and not all square matrices are invertible. I not positive so I'd like some help. Answered by Penny Nom. 





A matrix construction problem 
20050314 

From Marcelo: I want to know if is it possible to solve this problem:
I have an empty NxM matrix and I know totals (sum) by rows and totals by column.
Is there any algorithm to fill the matrix so that the summary of columns and rows gives the original values I have? Answered by Harley Weston. 





Construction of a cone 
20041120 

From John: I am a builder working on a project where I need to make a cone. It's a right circular cone with 15" base radius and slant angle of 30 degrees. I want to cut it out of flat sheet metal then bring the edges together to form the cone. Is this enough information? Answered by Penny Nom. 





Constructing a cone 
20040907 

From Steve: I am trying to build crayfish traps; one of the components is a cone shaped entry section.
The cone I want to make would be 12" in diameter at the base and 12" in height, from base to peak.
I need a formula to calculate the dimensions and a method of transferring the shape onto a flat piece of material.
Answered by Harley Weston. 





Constructing a triangle 
20040808 

From KV: HOW TO CONSTRUCT A TRIANGLE ABC, WHEN
ITS ALTITUDES AD,BE,CF ARE GIVEN Answered by Chris Fisher. 





Making a cone 
20031222 

From Tracie:
I am working on a craft project at home and I have been given the following information: 16" tall and 13" diameter at base, with 1 and 1/2 " opening at top.
Is there a basic formula for creating a cone with this info?
Answered by Claude Tardif and Penny Nom. 





A ruler and compass construction 
20030629 

From Mandy: I have been searching for instructions on how to do this using a compass. Can you please send instructions step by step on how to bisect a segment into any given number of segments. (example, a way that it will work for bisecting segment into 3, 4, or even 5 congruent parts) Answered by Penny Nom. 





Constructions of polygons 
20030103 

From Garrett: Our teacher just finished the constructions unit, and he mentioned briefly about odd sided figures such as pentagons and septagons, only that they're very hard. My question is, how do you draw, with a compass and a straight edge, a pentagon and septagon? Answered by Chris Fisher. 





Construct a pentagon 
20021212 

From Mary: We were wondering what the instructions/formula, stepbystep, is to make a pentagon. Answered by Chris Fisher and 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. 





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. 





Constructing the square root of 3 
20020607 

From Allan: I am a Math 7/8 teacher. I was wondering how you would show a student how to find the exact location of the square root of three on the number line using just a compass and a straight edge. Answered by Penny Nom. 





Matrix reconstruction 
20010719 

From Guy: Is there a way to get the sums of rows, columns and diagonals of an n x n matrix to reconstruct the original matrix? Answered by Walter Whiteley and Patrick Maidorn. 





Constructing an equilateral triangle 
20010414 

From Peggy: Please send directions to make an equilateral triangle in plane geometry. I want each student to draw two, cut them out, and place them together to form a Jewish Star. Answered by Penny Nom. 





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. 

