In 1897, Indiana physician Edwin J. Goodwin believed he had discovered a way to square the circle, and proposed a bill to Indiana Representative Taylor I. Record which would secure Indiana\u2019s the claim to fame for his discovery. About the time the debate about the bill concluded, Purdue University professor Clarence A. Waldo serendipitously came across the claimed discovery, and pointed out its mathematical impossibility to the lawmakers. It had only be shown just 15 years before, by the German mathematician Ferdinand von Lindemann, that it was impossible to square the circle because \u03c0 is an irrational number. This fodder became ignominiously known as the \u201cIndiana Pi Bill\u201d as Goodwin\u2019s result would force $\\pi = 3.2$.<\/p>\r\n
In this talk, we review this humorous history of the irrationality of $\\pi$. We introduce a method to compute its digits, present Lindemann\u2019s proof of its irrationality (following a simplification by Miklo \u0301s Laczkovich), discuss the relationship with the Hermite-Lindemann-Weierstrass theorem, and explain how Edwin J. Goodwin came to his erroneous conclusion in the first place.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","protected":false},"excerpt":{"rendered":"
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