A reporter at the Wisconsin State Journal called me the other day with a really good question. He had heard that pi had been computed to ten trillion decimal places. And he wanted to know: how could you possibly measure a circle that precisely?

So how did he know to call me? Because I’m on the experts list, which UW-Madison’s public relations office set up to give journalists the opportunity to consult a Wisconsin professor on just about any subject. Topics of current news interest get promoted to the front: on today’s front page we’ve got the professor who can talk about Kim Jong-Il, the professor who can talk about the Supreme Court’s decision to take up the Arizona immigration law, and the professor who can talk about the Scott Walker recall. (I have a feeling that last guy is going to be on the front page for a while.)

Such a simple idea, but such a good one! The UW-Madison *ought* to be a resource for Wisconsin journalists — and everybody else in Wisconsin, for that matter. Good for the PR office for making it as easy as possible to reach faculty who want to face the public and share what they know.

Oh: here’s the article about pi in the WSJ, by Dave Tenenbaum. I thought it came out well!

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Jordan — you fooled me with WSJ. I guess I have been in NYC too long.

I think you are being too harsh with the comment:

“In geometry, pi (3.14159….) is defined as the ratio of circumference to diameter, and “if this is the only definition of pi, then computing it to many decimal places would be impossible,” said Jordan Ellenberg, professor of mathematics at UW-Madison. Logically, this would amount to “garbage in, and garbage out,” because the result of a calculation cannot be more precise than the starting terms.”

Archimedes did pretty well with this method — “On the measurement of the circle” may be one of the four or five greatest math papers ever written. Archimedes worked with an inscribed and circumscribed 96-gon — whatever you think of this method, it is certainly not “garbage in, garbage out”. You can get more decimals of accuracy by continuing to double the number of sides, using his recursion for the side length. This requires the careful approximation of square roots — we have no idea how Archimedes obtained his rational approximations, although perhaps he had derived the basics of the theory of continued fractions from the Euclidean algorithm.

Your comment hinges on the meaning of the word “many”. Maybe that’s a good subject for another article in the WSJ!

You make a good point! I think I was responding to Tenenbaum’s original question about measuring physical circles. Of course, my definitional fig leaf can be that “the limit of the ratio of perimeter to long diagonal of an n-gon as n goes to infinity” is not LITERALLY the same definition as “ratio of circumference to diameter…!”

Dear Dick,

I was also momentarily surprised that a writer from the WSJ was using the U of W expert list as a resource! Is it really true that Archimedes’s methods remain a mystery?

Best wishes,

Matt