







Solides d’Archimède 
20140429 

Clémentine pose la question : 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 Chris Fisher lui répond. 





Le salinon d'Archimèdre 
19990311 

Don Craig pose la question : 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. Harley Weston lui répond. 





An arched window 
20170724 

Gerry pose la question : 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" Penny Nom lui répond. 





A parabolic arch 
20170105 

Rand pose la question : 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 Harley Weston lui répond. 





A search area 
20160813 

tammy pose la question : if your searching an area and you go 300 km from point A and search 380° what or how much area would you search? Penny Nom lui répond. 





Heights at various points along an arc 
20160415 

Isiah pose la question : 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 Penny Nom lui répond. 





Shooting a ball at a target 
20160216 

Thys pose la question : 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) Harley Weston lui répond. 





A parabolic arch 
20151130 

Muhammad pose la question : 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 Penny Nom lui répond. 





Archimedes, Euclid and "Circular Reasoning" 
20151115 

Ron pose la question : 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. Chris Fisher lui répond. 





The distance over a Quonset 
20150820 

jane pose la question : total base of hemisphere is 30 ft
apex height is 20 feet
what is total length over dome Penny Nom lui répond. 





Archimedes Burning Mirror 
20120717 

Frakeetta pose la question : 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? Robert Dawson lui répond. 





A parabolic arch 
20120104 

Swathi pose la question : 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 Penny Nom lui répond. 





How much work is done? 
20111015 

Jean pose la question : "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 ?" Penny Nom lui répond. 





Find the rate at which the searchlight rotates 
20110417 

Meredith pose la question : 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. Penny Nom lui répond. 





Will the ball clear the tree? 
20101114 

MK pose la question : 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? Brennan Yaremko lui répond. 





Body measurements 
20100406 

Amirul pose la question : 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?? Robert Dawson lui répond. 





The height of an arch 
20100102 

kamer pose la question : given the radius 1.696 also the cord length 1.958 find the height between the cord and the arch. Penny Nom lui répond. 





The layout of an arch 
20090818 

Steven pose la question : 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 Stephen La Rocque lui répond. 





An arched or round top window 
20090407 

Dale pose la question : 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. Harley Weston lui répond. 





The height of an arc at the peak 
20090401 

Ed pose la question : What is the term used to describe the height of an arc at the peak? Stephen La Rocque lui répond. 





A parabolic arch 
20090328 

Jeni pose la question : 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. Penny Nom lui répond. 





Archimedes' formula for parabolic arches 
20090123 

La pose la question : Use calculus to verify Archimedes' formula for y=9x^2. Prove Archimedes' formula for a general parabolic arch. Harley Weston lui répond. 





An arch is in the form of a semi ellipse 
20081103 

jessica pose la question : 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. Penny Nom lui répond. 





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

megan pose la question : 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! Penny Nom lui répond. 





The length of an arc 
20080516 

Don pose la question : I am trying to determine the length of an arch with a two foot backset from 32 foot frontage. Harley Weston lui répond. 





A parabolic arch 
20080214 

Angela pose la question : 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? Penny Nom lui répond. 





A large concrete shape 
20080116 

Keith pose la question : 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? Stephen La Rocque lui répond. 





An arched entry 
20071128 

amber pose la question : 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? Stephen La Rocque lui répond. 





The radius of an arch 
20071110 

Mark pose la question : 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". Harley Weston lui répond. 





Completing the square 
20071101 

Mark pose la question : 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. Stephen La Rocque lui répond. 





parabolic arch 
20071024 

ABHILASH pose la question : How find parabolic arch perimeter. Harley Weston lui répond. 





Parabolic arch 
20071009 

Nisa pose la question : 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. Stephen La Rocque lui répond. 





The perimeter of a regular polygon 
20070918 

Ashwynn pose la question : why does the area of regular polygons with a perimeter of 1000m increase as the number of sides increase? Stephen La Rocque lui répond. 





Babylonian geometry 
20070617 

marleen pose la question : 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. Stephen La Rocque lui répond. 





A steel arc 
20070531 

Huw pose la question : 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. Penny Nom lui répond. 





A cabinet with an arched front 
20070409 

Joe pose la question : 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 Penny Nom lui répond. 





An arched opening for a large doorway 
20070408 

Richard pose la question : 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? Stephen La Rocque lui répond. 





A parabolic arch 
20070329 

A student pose la question : 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. Stephen La Rocque lui répond. 





The width of an arch 
20070328 

Brad pose la question : A parabolic arch satisfies the equation y= 16  0.25x^2 for y >= 0. Find the width w of the arch. Penny Nom lui répond. 





A roadway over a river 
20070312 

Taranjeet pose la question : 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 Penny Nom lui répond. 





Can the trailer safely pass under the bridge? 
20070102 

Jim pose la question : 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? Stephen La Rocque lui répond. 





Splitting A Circle Evenly 
20061220 

Joe pose la question : 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. Penny Nom lui répond. 





The radius of an arch 
20061115 

Kelly pose la question : I am trying to achieve an arc height of .375 on the length of 17.375. Penny Nom lui répond. 





A fountain of water jets forms parabolic arches 
20060503 

Jennifer pose la question : 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? Stephen La Rocque lui répond. 





A parabolic arch 
20060502 

Mike pose la question : 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? Stephen La Rocque lui répond. 





Framing an arched wall 
20050812 

Mike pose la question : 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? Penny Nom lui répond. 





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

Lauren pose la question : 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? Penny Nom lui répond. 





Marching legion 
20040424 

Art pose la question : 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? Penny Nom lui répond. 





A parabolic arch 
20040119 

Teresa and Robyn pose la question : 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 Penny Nom lui répond. 





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

Bill pose la question : 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? Harley Weston lui répond. 





Bridges and parabolas 
20001118 

Lauren pose la question : 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. Harley Weston lui répond. 





Cairo tesselation and Archimedean duals 
20000621 

Joyce DuVall pose la question : 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? Penny Nom lui répond. 





Calculus Research Questions 
20000522 

William Wright pose la question : 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. . . . Harley Weston lui répond. 





Volume of a sphere 
20000521 

Kevin Partridge pose la question : 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? Harley Weston lui répond. 





A roll of paper 
20000115 

Richard pose la question : 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. Chris Fisher and Harley Weston lui répond. 





Linear programming and optimization 
19990409 

Shams pose la question : What is Linear programming and optimization? Jack LeSage and Penny Nom lui répond. 





Operations Research 
19981008 

Lisa Barrett pose la question : What is the history of operations research and the study of linear programming? Judi McDonald lui répond. 





Approximating pi. 
19961104 

Ben Dixon pose la question : How do you calculate Pi? Do you have to somehow combine the equation for a circle with the formula for the circumference? Chris Fisher lui répond. 

