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The Baffling and Beautiful Wormhole Between Branches of Math

•, By Lee Simmons

What's the deal with Euler's identity? Basically, it's an equation about numbers—specifically, those elusive constants π and e. Both are "transcendental" quanti­ties; in decimal form, their digits unspool into infinity. And both are ubiquitous in scientific laws. But they seem to come from different realms: π (3.14159 …) governs the perfect symmetry and closure of the circle; it's in planetary orbits, the endless up and down of light waves. e (2.71828 …) is the foundation of exponential growth, that accelerating trajectory of escape inherent to compound interest, nuclear fission, Moore's law. It's used to model everything that grows.

Enter Leonhard Euler, the one-eyed Swiss genius whom Frederick the Great lovingly called "our Cyclops." What Euler showed, in his 1748 book Introduction to Analysis of the Infinite, is that π and e are deeply related, but in a very weird way. They're connected in a dimension perpendicular to the world of real things—a place measured in units of i, the square root of –1, which of course doesn't … exist. Mathematicians call it an imaginary number.

1 Comments in Response to

Comment by Dennis Treybil
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This article mentions Euler's identity. This mathematical concept was mentioned also in a recent episode of "Person of Interest" - a series that Ernest brought up in the 3rd hour of today's broadcast. That's where I heard of Euler's identity. Likewise, I first heard of Fibonacci in a math-centered tv series starring Fred "Herman Munster" Gwynne. How does an an eat an elephant? One bite at a time. So, these bits and pieces seem to stick . . . . DC Treybil

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