The Pythagorean, Hippasus, is credited with the discovery that the - TopicsExpress

The Pythagorean, Hippasus, is credited with the discovery that the side of a square and its diagonal are incommensurable (i.e. a square of length 1 has a diagonal with irrational length). This showed that the whole numbers are inadequate to represent the ratios of all geometric lengths. This discovery established the supremacy of geometry over arithmetic in all subsequent Greek mathematics. For all the trouble that Hippasus caused, the Pythagoreans supposedly took him far out into the Mediterranean and tossed him overboard to his death - thereby indicating the dangers inherent in free thinking, even in the relatively austere discipline of mathematics in those times!

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