Even more bizarre, IMHO, is the fact that in the volume formula for n dimensions, it isn't pi itself, but sqrt(pi), that is important. I don't think that the Greeks figured that part out. If you go through all the formulae in a large book -- e.g., Stegun, et al -- I think that "2pi" shows up more often than "pi". Sooner or later, we're bound to run up against a civilization that chose differently which to commemorate with a name. At 04:08 PM 4/30/2008, Dan Asimov wrote:
Bernie asks:
<< . . . the area of a circle is 3.14... times the square of the radius and the volume of a sphere is 4.18... times the cube of the radius. . . . But when did mathematicians realize that those weren't two separate gnarly constants, but actually "reflections" [if you will] of a single underlying constant? I don't think the Greeks had enough math machinery to figure all that out, did they? . . .
Yes, the fact that the ratio of the volume of a sphere to the volume of the circumscribed cylinder is 2/3 was one of Archimedes' proudest achievements: This is said to be inscribed on his gravestone.
--Dan