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Good Math by Mark C. Chu-Carroll

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The Argh! Moments of Irrational Numbers

According to legend, the first disappointment involving the irrational numbers happened in Greece around 500 BC. A rather brilliant man by the name of Hippasus, who was part of the school of Pythagoras, was studying roots. He worked out a geometric proof of the fact that the square root of 2 could not be written as a ratio of integers. He showed it to his teacher, Pythagoras. Pythagoras, like so many other mathematicians, was convinced that numbers were clean and perfect and he could not accept the idea of irrational numbers. After analyzing Hippasus’s proof and being unable to find any error in it, he became so enraged that he drowned poor Hippasus.

A few hundred years later, Eudoxus worked out the ...

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