pi is a beautiful transcendental.
The FIRST logo elements triangle, circle, and square, are projections of three interesting solids -- a cone with the same diameter and height, a sphere of that diameter, and a cylinder of that diameter and height. Volumes of these three solids are in 1:2:3 proportion, as discovered by Archimedes. (see the attachment)
A few years ago, I made a
demo for the Cork Plug teaser: find one solid object that will completely plug holes of the shapes used in the FIRST logo. Volume of the (maximal) cork plug is more than that of the cone, and less than that of the sphere.
Mysteriously, pi keeps popping up in these formulae ....
__________________
Richard Wallace
Mentor since 2011 for FRC 3620 Average Joes (St. Joseph, Michigan)
Mentor 2002-10 for FRC 931 Perpetual Chaos (St. Louis, Missouri)
since 2003
I believe in intuition and inspiration. Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world, stimulating progress, giving birth to evolution. It is, strictly speaking, a real factor in scientific research.
(Cosmic Religion : With Other Opinions and Aphorisms (1931) by Albert Einstein, p. 97)
A challenge to those of you grumbling about the refereeing this year: Be a referee next year. - Alan Anderson [more] 
15-06-2011, 16:17
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