Apparently not wittingly, but they dit work on approximations to the root of 2. Babylonians had the basic concept of pythagoras's theorem, but the greeks gave birth to irrational numbers as such. It was one of pythagoras's pupils - Hipposus - who first struggled with the root of 2 and came to the conclusion that some numbers where irrational. Faced with such irrationality from one of his pupils, Pythagoras ordered Hipposus to be drowned.
(I can think of a student or two I may have done something similar to for lesser reasons ;).
http://www.geocities.com/mathimoh/irrational.html
http://members.aol.com/bbyars1/first.html
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Real_numbers_1.html | [reply] |

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