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Euler's Gem by David S. Richeson

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CHAPTER 3

THE FIVE PERFECT BODIES

There are always antecedent causes. A beginning is an artifice, and what recommends one over another is how much sense it makes of what follows.—Ian McEwan, Enduring Love1

Modern geometry, and indeed much of modern mathematics, can trace its roots back to the work of the Greeks. During the period from Thales (c. 624-547 BCE) to the death of Apollonius (c. 262-190 BCE), the Greeks produced an astonishing body of mathematical works, and the names of many of the scholars of this era are familiar to schoolchildren everywhere: Pythagoras, Plato, Euclid, Archimedes, Zeno, and so on.

Although the mathematics from Egypt, Mesopotamia, China, and India may have influenced the Greeks, they quickly made the discipline their ...

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