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How did the ancient Greeks discover that the ratio of a circle's circumference to its diameter is constant? It does not seem so intuitive. Thanks!

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marked as duplicate by apnorton, Dominic Michaelis, Henning Makholm, rschwieb, Paul Apr 16 '13 at 20:50

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I don't know the answer [hence why I'm posting this as a comment], but I suspect that it wasn't proved rigorously [at least, not at first]. Rather, I suspect they'll have tested it on loads of circles and thought 'wow, this is, like, the same each time, lol'. But I'm open to being corrected. – Clive Newstead Apr 16 '13 at 20:31
It seems perfectly obvious to me. Like so many important discoveries $-$ Darwin's theory of evolution, for instance $-$ it only needed to be stated. – TonyK Apr 16 '13 at 20:31
How do you know the ratio of a square's circonference to its side is 4? – Raskolnikov Apr 16 '13 at 20:36
@CliveNewstead The classics would be so much more entertaining if they were interspersed with "lol" and "omg" :) – rschwieb Apr 16 '13 at 20:56
up vote 1 down vote accepted

Probably they used an intuitive (or maybe exact) idea of geometric similarity.

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