>Pythagoreans didn't ever discover irrationals, and could not have discovered >irrationals given their concept of number. > >What was discovered (between 415 & 405 BC, and not likely to have been by a >Pythagorean) was the existence of non-co-measurable magnitudes, which are not >irrationals, but a pair-wise property of two magnitudes on not having a common >unit. Thus root-2 and 2 x root-2 are co-measurable... which is why non-co->measurables are not irrationals.
This opens the question of who it was who discovered that square roots etc. could not in general be represented by rational numbers, or who discovered non-co-measurable magnitudes.
Was it the Babylonians, who among other accomplishments had the quadratic formula? Or the Egyptians, who worked on cubic equations?
James A. Landau test engineer Northrop-Grumman Information Technology 8025 Black Horse Pike, Suite 300 West Atlantic City NJ 08232 USA
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