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Euler's Gem by David S. Richeson

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CHAPTER 10

LEGENDRE GETS IT RIGHT

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It’s like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.—Freeman Dyson1

The second published proof of Euler’s polyhedron formula, and the first to meet today’s rigorous standards, was given by Adrien-Marie Legendre. Legendre was a French mathematician who belonged to both the Académie des Sciences in Paris and the Royal Society of London. He published in several areas, but his most important contributions were to number theory and the theory of elliptic functions. ...

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