Now I am interested in Pi: It is rigidly linked to the beautiful circle, that consummate representation of perfect symmetry. But it can masquerade in many forms. It appears as a beautiful infinite sum, as an infinite product, or even as an infinitely repeated fraction. Through the wave formulas for light and sound, it tells us which colors should appear in a rainbow and how middle C should sound on a piano. It explains which direction the proverbial needle will fall when it hits the haystack. You will find it describing the morphology of the apple and the energy of stars. It sits deep in the wave functions describing the quantum state of the hydrogen atom. It even plays a significant role in analyzing survey predictions for the next president. And it’s entrenched in Heisenberg’s uncertainty principle, the equation that tells us just how precisely we can ever know the state of the universe. My favorite, and one of the most surprising relations, is about how pi connects river flow with bird flight. Imagine a river flowing in uniformly erodible sand under the influence of a gentle slope. The sand can be moved—though not easily—by the pressures of the river flow. Over time, the river’s actual length, divided by the straight-line distance from beginning to end (that is, as the crow flies), will tend toward pi. If you guessed that the circle might be a cause, you would be right. Once again, there is that ubiquitous pi lurking about. Over time, the edges of the river tend to dredge themselves to smoothen out any sharp curves. Pi, and by extension circles, are deeply rooted in our perception of the universe. As I explain in my book Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers, over the centuries many people approximated pi, starting with the Babylonians. Archimedes in the 2nd century B.C. got it accurately to three decimal places. By the 17th century, the German-Dutch mathematician Ludolph van Ceulen, who spent a lifetime calculating pi, succeeded in getting it to a colossal 35 decimals, 3.14159265358979323846264338327950288... , which is engraved on his tombstone. - Slate
Posted on: Sat, 15 Mar 2014 14:15:41 +0000
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