Mathematics in the 21st Century by Scientific American Editors

Author:Scientific American Editors [Editors, Scientific American]
Language: eng
Format: epub
ISBN: 9781948933124
Publisher: RosenGroup
Published: 2019-08-20T05:00:00+00:00

Why call them periods? In the simplest cases, that is literally what they are: the distance before something repeats. Thinking back to high school, you might remember grappling with sines and cosines. You might even remember that you can put them together with imaginary numbers (the square roots of negative numbers—in other words, numbers that would not normally exist) using Euler’s formula: eix = cos (x) + i sin (x) (here e is a constant, and i is the square root of -1). All three of these—sin (x), cos (x), and eix—have period 2Π: if you let x go from 0 to 2Π, the function repeats, and you get the same numbers again.

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