Math Central - mathcentral.uregina.ca
Quandaries & Queries
Q & Q
. .
topic card  



list of
. .
start over

10 items are filed under this topic.
Archimedes, Euclid and "Circular Reasoning" 2015-11-15
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.
Archimedes Burning Mirror 2012-07-17
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.
How much work is done? 2011-10-15
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.
Archimedes' formula for parabolic arches 2009-01-23
From La:
Use calculus to verify Archimedes' formula for y=9-x^2. Prove Archimedes' formula for a general parabolic arch.
Answered by Harley Weston.
The perimeter of a regular polygon 2007-09-18
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.
The volume of a sphere. Why 4/3? 2005-05-30
From Lauren:
You know when you find the volume of sphere? I know the formula is V= 4/3 pi r3 but why do they use 4/3?
Answered by Penny Nom.
Volume of a sphere 2000-05-21
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 2000-01-15
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.
Approximating pi. 1996-11-04
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.
Le salinon d'Archimèdre 1999-03-11
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 semi-circles. 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 semi-circle is constructed on AE as diameter (let's say above AE).

Two more semi-circles are then constructed with diameters AB and DE on the same side of the line AE as the first semi-circle (above it). Finally, a fourth semi-circle is constructed on diameter BD, this time on the opposite side of the line AE from the others (i.e. below the line).

These semi-circles 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.




Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.



Home Resource Room Home Resource Room Quandaries and Queries Mathematics with a Human Face About Math Central Problem of the Month Math Beyond School Outreach Activities Teacher's Bulletin Board Canadian Mathematical Society University of Regina PIMS