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Euler's Gem by David S. Richeson

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CHAPTER 12

CAUCHYS FLATTENED POLYHEDRA

Cauchy is mad and there is nothing that can be done about him, although, right now, he is the only one who knows how mathematics should be done.—Niels Abel1

In the hundred years after Euler’s proof of his polyhedron formula, there were many new proofs and a variety of generalizations to exotic polyhedral shapes. The first significant generalization came from Augustin-Louis Cauchy, who also gave an ingenious new proof.

Cauchy was born in Paris in 1789. He was the eldest son of a senior government administrator. Although his family was displaced during the Reign of Terror, his father saw that he received a good education. As a youth he became acquainted with the mathematicians Pierre-Simon Laplace (1749–1827) ...

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