Infinite Powers: How Calculus Reveals the Secrets of the Universe

by Steven H. Strogatz

This unexpected link between music (the harmony of this world) and numbers (the harmony of an imagined world) led the Pythagoreans to the mystical belief that all is number.

By combining the symbols of algebra with the power of infinity, he found a way to represent any curve as a sum of infinitely many simpler curves described by powers of a variable x, like x2, x3, x4, and so on. With these ingredients alone, he could cook up any curve he wanted by putting in a pinch of x and a dash of x2 and a heaping tablespoon of x3. It was like a master recipe and a universal spice rack, butcher shop, and vegetable garden, all rolled into one.

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