After the class have exhausted their energies on the theorem of the right triangle, tell them something about its discoverer – how Pythagoras, jubilant over his great accomplishment, sacrificed a hecatomb to the Muses who inspired him.
Let us suppose that we have set the problem of finding a solution to the equation This is a problem for which the Babylonians around 1700 BC found the excellent approximation ...This is the identical problem which Pythagoras asserted had no fractional solution and in whose honor he was supposed to have sacrificed a hecatomb of oxen the problem which caused the existentialist crisis in ancient Greek mathematics. The exists (as the diagonal of the unit square); yet it does not exist (as a fraction)!
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