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Now be honest-wouldn't you have expected e^i*pi to be (a) gibberish aling the lines of "elephant inkpie," or, if it were mathematically meaningful, to be (b) an infinitely complicated irrational number? Indeed, e^i*pi is a transcendental number raised to an imaginary transcendental power. And if (b) were the case, surely e^i*pi would not compute no matter how much computer power were available to try to pin down its value. As you know, neither (a) nor (b) is true, because e^i*pi = -1. (I suspect the fact that both (a) and (b) are provably false is the reason that Benjamin Peirce, the nineteenth-century mathematician, found Euler's formula (or a closely rekated formula) "absolutely paradoxical.") In other words, when the three enigmatic numbers are combined in this form, e^i*pi , they react together to carve out a wormhole that spirals through the infinite depths of number space to emerge smack dab in the heartland of integers. It's as if greenish-pink androids rocketing toward Alpha Centauri in 2370 had hit a space time anomaly and suddenly found themselves sitting in a burger joint in Topeka, Kansas, in 1956. Elvis, of course , was playing on the jukebox.
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David Stipp (A Most Elegant Equation: Euler's Formula and the Beauty of Mathematics)