Pi shows up a lot in geometry. I was wondering when "we" (ahem) realized that it was just one underlying constant. For example, 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. It is already profound discovering that those ratios are fixed [and to be able to calculate a bunch of digits of them]; I don't know if he did or not, but I can' easily see Archimedes managing to calculate a bunch of digits of the 4.18... constant even as he did for the 3.14. one]. 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? [that is, that the ratio of those two constants is exactly 3:4. Or that the ratio of the radius of a circle to its curcumferenace is really just exactly twice the ratio of the square of the radius of the circle to its area; 3.14... and 6.28... will certainly *look* like 1:3 [not clear the 3:4 ratio is as obvious..:o)], but could they actually 'know' that enough to say that that was really "proven", in some sense? If not the greeks, then when did we figure that out? /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--