All is number

The punishment for what was perhaps the first proof of impossibility was severe. 

Historians believe that in the fifth century BCE, Hippasus of Metapontum, a follower of the cult leader Pythagoras, discovered that it is impossible to find a line segment that can be placed end-to-end to measure both the side and the diagonal of a regular pentagon. 

Today we say that the length of a diagonal of a regular pentagon with side length 1 —the golden ratio, ϕ = 12 (1 + 5–√) —is “irrational.” 

Hippasus’ discovery flew in the face of the Pythagorean credo that all is number, so, according to legend, he was either drowned at sea or banished from the Pythagoreans.


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