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Numerical Mysteries/  /August 10, 2005

Why does Jason Kottke say that it's a coincidence that humans discovered circles first and pi later?

Isn't pi defined as the ratio of a circle's circumference to its diameter? A trip to wikipedia says yes. Checking Wolfram's Mathworld (a poor man's wikipedia) I see the same.

Pi is precisely derived from the circle, and nothing else. The number denoted by pi is just one particular number in an infinitely-infinitely large continuum of real numbers. How do we find the one called pi? Well, first you get a circle, then you measure its circumference...

I'm baffled as to why people keep searching for some message from God in the decimal digits of pi. One wonders why they never seem to look for messages in the binary digits, or the digits in base 17. Or then again, why the expansions of e, or the golden ratio, are not studied with the same devotion. Even then, it should strike as apointless mysticism to search for patterns in this expansions. Perhaps 7 appears surprisingly often, as they say. What of it? It would not be so great a discovery as the fact that it is possible to slice a sphere into finitely-many pieces and put them back to form two spheres the same size (this does require the Axiom of Choice, however).

More mysterious than all these mysteries is why the New Yorker editors manage to publish pieces about everything under the god-forsaken Sun, from troop movements to the selling of cheese, to the travails of an Arctic swimmer, but in ten years they can only find it in themselves to publish two or perhaps three pieces about the fascinating world of mathematics, and twice about the same two crackpots. There is certainly a pattern there.

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Comments

Much more interesting than the decimal expansion of pi is the continued fraction expansion of pi.

It is similarly interesting to note that the continued fraction expansion of the golden ratio is [1,1,1,1,1,...] which really gives some insight to the character of the number, and so might pi's continued fraction expansion.

—posted by Jim at August 10, 2005 8:49 PM

While I am a big fan of even numbers, the ancients ascribed sacred meaning to many of the prime numbers (3, 7, 13, 19, etc).

smiles, jen ;o)

p.s. Are you in Edinburgh, yet?

—posted by Ms. Jen at August 12, 2005 12:00 AM

Not yet!

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