This originally appeared on the GEnie Space and Science Round Table

A Brief History of Pi

by Petr Beckmann

Reviewed by Michael J. Mehl

Pi has always fascinated ordinary people as well as mathematicians. In this legendary book, Petr Beckmann gives an entertaining account of the development of the concept of Pi, and of methods for its calculation. Along the way he talks about Babylonian guesses for Pi, Mayan positional notation, Euclid's geometry, and Euler's theorems, modern "circle squarers", and the interesting bill once passed by the Indiana House of Representatives, the source of the urban legend of the "legislature which set pi = 3."

Remember High School Geometry? There's a lot of that in here. Beckmann throws some light on the "compass and straight-edge" restrictions the Greeks imposed. They weren't just arbitrary restrictions, they formed the physical backdrop for Euclid's five postulates, in particular the fifth postulate. And he points out that if you give up the Greek adversion to infinity you can, in fact, square the circle with compass and straight-edge, (in an infinite number of operations).

Beckmann also discusses "the digit hunters", the people who calculated Pi to thousands of digits, using Taylor series expansions for inverse hyperbolic functions obscure formulas such as

        pi/4 = 4 arctan 1/5 - arctan 1/239 

He also discusses computer calculations of pi. Of course, since this book was written in 1970, the "modern" computers discussed here could only calculate pi to about 500,000 places. (For the first 1,000,000 digits of pi, see the file MEGOFPI.ZIP, number 3130 in the library.)

That's the interesting part of the book. The fun part of the book is Beckmann's diatribe. This book isn't just about Pi, it's a discussion of everything Beckmann sees as wrong with Western Civilization since the Achaens invaded the Peloponnesus. First to get the Beckmann treatment is Pythagoras, "a mathematician to a much lesser degree than he was a mubo- jumboist." Aristotle ("shockingly ignorant of the science of his time") gets it next. Archimedes, the preeminant scientist of the ancient world, gets very favorable press: Beckman makes the valid point that he didn't shun working with his hands, unlike most Greek thinkers. In fact, he enjoyed making models to help guide his mathematical proofs.

The Romans emerge from this as the "thugs" of the ancient world. Beckmann has some telling points. In the chapter "The Roman Pest", which has nothing to do with the history of Pi, he points out the parallels between Nazi, Soviet, and Roman architecture: big, proud, and boastful. And there's this: "In a healthy society, enginering design gets smarter and smarter; in gangster states, it gets bigger and bigger." If you've got a friend whose into the type of military SF which tries to rebuild the Roman Empire, stear him to this chapter in Beckmann's book. All of this is way overdone, of course, but Beckmann does make some valid points. The constant bombast does tend to remind you of the Rush Limbaugh show, but Beckmann can outthink Rush and Newt combinded, so it is entertaining.

If there's a fault to this book, aside from Beckmann's bombast, it is that it is written for the Heinlein "competent man", the one who can extract cube roots while skinning a deer. In other words, the reader is supposed to know all of this stuff already, or at least the principles. If you don't know it, Beckmann's not going to tell you where to find it, you're supposed to be bright enough to find it yourself. As a result, if you're going to delve into the math you are going to have to dig out your old High School geometry book and start proving theorems. This condenscending attitude did give me a kick in the bottom -- I've rediscovered two proofs of the Pythagorian theorem, something I'd forgotten how to prove over the last 25 years.

This book is highly recommended, if the rhetoric doesn't bother you. I just hope you can find it. A: T: P: . "For information, write St. Martin's Press, Inc.; 175 Fifth Ave.; New York, NY 10010." $9.95 at Borders, in a Digest size paperback.

Author:     Petr Beckmann
Title:      A History of Pi
Publisher:  Golem Press, 1971 "For information, write St. Martin's
            Press, Inc.; 175 Fifth Ave.; New York, NY 10010."
List Price: $9.95 (Current price at Borders and Crown Books)

Want to calculate Pi for yourself? Check out the Miraculous Bailey-Borwein-Plouffe Pi Algorithm and then download this Fortran program.
Any opinions expressed here are my own, and are not necessarily those of any of my past, present, or future employers, friends, family, or associates.

© 1996 by Michael J. Mehl

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