A HISTORY OF PI

by Petr Beckmann

Preface

The history of pi is a quaint little mirror of the history of man. It is the story of men like Archimedes of Syracuse, whose method of calculating pi defied substantial improvement for some 1900 years; and it is also the story of a Cleveland businessman, who published a book in 1931 announcing the grand discovery that pi was exactly equal to 256/81, a value that the Egyptians had used some 4,000 years ago. It is the story of human achievement at the University of Alexandria in the 3rd century B.C.; and it is also the story of human folly which made mediaeval bishops and crusaders set the torch to scientific libraries because they condemned their contents as works of the devil.

Being neither an historian nor a mathematician, I felt eminently qualified to write that story.

That remark is meant to be sarcastic, but there is a kernel of truth in it. Not being an historian, I am not obliged to wear the mask of dispassionate aloofness. History relates of certain men and institutions that I admire, and others that I detest; and in neither case have I hesitated to give vent to my opinions. However, I believe that facts and opinion are clearly separated in the following, so that the reader should run no risk of being overly influenced by my tastes and prejudices.

Not being a mathematician, I am not obliged to complicate my explanations by excessive mathematical rigor. It is my hope that this little book might stimulate non-mathematical readers to become interested in mathematics, just as it is my hope that students of physics and engineering might become interested in the history of the tools they are using in their work. There are, however, two sure and all too well tried methods of how to make mathematics repugnant: One is to brutalize the reader by assertions without proof; the other is to hit him over the head with epsilonics and proofs of existence and unicity. I have tried to steer a middle course between the two.

A history of pi containing only the bare facts and dates when who did what to pi tends to be rather dull, and I thought it more interesting to mix in some of the background of the times in which pi made progress. Sometimes I have strayed rather far afield, as in the case of the Roman Empire and the Middle Ages; but I thought it just as important to explore the times when pi did not make any progress, and why it did not make any.

The mathematical level of the book is flexible. The reader who finds the mathematics too difficult in some places is urged to do what the mathematician will do when he finds it too trivial: Skip it.

This book, small as it is, would not have been possible without the wholehearted cooperation of the staff of Golem Press, and I take this opportunity to express my gratitude to every one of them. I am also indebted to the Archives Division of the Indiana State Library for making available photostats of Bill 246, Indiana House of Representatives, 1897, and to the Cambridge University Press, Dover Publications and Litton Industries for granting permission to reproduce copyrighted materials without charge. Their courtesy is acknowledged in the notes accompanying the individual figures.

I much enjoyed writing this book, and it is my sincere hope that the reader will enjoy reading it, too.
Boulder, Colorado
August 1970 Petr Beckmann

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