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Euler's Gem by David S. Richeson

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CHAPTER 8

PLATONIC SOLIDS, GOLF BALLS, FULLERENES, AND GEODESIC DOMES

Mathematics is concerned only with the enumeration and comparison of relations.—Carl Friedrich Gauss1

Mathematicians do not study objects, but relations between objects.—Henri Poincaré2

“That’s great, but what’s it good for?” the skeptical student asks, sarcasm dripping from his voice. Beauty is a wonderful trait, but some say usefulness is a more important measure of the worth of a theorem. What is Euler’s formula good for?

That is a fair question to ask of any mathematical theorem. Euler’s formula is more than just an elegant theorem. In the chapters that follow we will present many applications of Euler’s formula. Most will require constructing the appropriate framework ...

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