A History of Pi

If you don't quite understand what this book is about, much of it will read like a parade of Petr Beckmann's pet crotchets. (A partial list: he likes Archimedes, smart engineering, and political liberty; he despises Aristotle, the Roman Empire, and the Soviet Union.) Some readers may object to this sort of thing in what purports to be a history of mathematics. But I enjoy it, in part because I mostly agree with him and in part because it's not _just_ a parade of his pet crotchets.

Beckmann is treating the history of pi as a microcosm of the history of science and human freedom. Mathematics isn't pursued in a vacuum, and one of Beckmann's overarching concerns in this volume is to argue that mathematical (and scientific) advances occur only when political liberty is realized.

In support of this thesis he presents a marvelous array of blundering bureaucrats and asinine apparatchiks who couldn't engineer their way out of a wet paper sack. (You will, for example, find out exactly _which_ U.S. state legislature tried to round off the value of pi by law.) His remarks on Roman and other imperial "engineering" are sheerly delightful; his gibes at Aristotle tend to hit their mark although I think he fails to do the philosopher justice overall; his skewering of people who waste time calculating the value of pi to umpteen-bajillion decimal places is a joy to read.

He also does a nice job presenting the positive history of pi -- that is, the genuine advances made when people like Gauss and Euler enjoyed sufficient intellectual liberty to do real mathematics without having to perform constant obeisance to self-important imperial stupidity. Contrary to what some reviewers have suggested, there _is_ a good deal of actual history of mathematics here.

But don't buy the book if you don't like writers who present firmly-held opinions forcefully. Beckmann is an interesting fellow: he's an escapee from Communist Eastern Europe, he was for a time associated with Ayn Rand's silly "Objectivist" movement, and he has edited a journal of anti-Einsteinian physics. If you don't like your intellectual medicine in strong doses, a little bit of Beckmann will go a long way.

As for me, I enjoy him thoroughly. And whether you like him or not, you shouldn't mistake him for a crank. His "history of pi" is an eloquent argument for freedom and against empire.


"AHOPi" Its all about that number...3.1415926535897932 etc.   March 30, 2005
Russell A. Rohde MD (West Covina, California USA)
8 out of 9 found this review helpful

"A History of Pi", by Petr Beckmann, NY:Barnes & Noble Books,3rd. Ed.,-ISBN 0-88029-418-3, HC 200 Pg. (8.2" x 5.5") includes 3 Pg. Notes, 3 Pg. Biblio., 2 Pg. Chrono., 3 Pg. Index & 2 Pg. Pi...to 10,000 decimal places (whew!).

We are given 18 Chapters: includes: - origins of numbers, Greeks, Euclid, Romans, Archimedes, etc., then digital hunters, Newton, Euler, Monte Carlo method, Transcendence of Pi, those 'modernists' (q.v.) & the computer age. Each & every chapter (save Chap. 5) is endowed & clothed by figures, formulae & graphs for those readers adequately equipped in geo., trig., logs, & the calculus, etc. As a whole, this is an intensely interestng chronological history of Pi & of those renowned mathematicians & academicians who invented, exploited or expounded on Pi & related matters. Especial attention is given to recounting the Romans more as murderers & thugs rather than mathematicians & thinkers (Chap. 5). Some religious commentary is incidental & unrewarding.

The author shuffles, leaps, or waltzes from tantalizing tidbits of information we've either mislearnt, learnt or long forgotten in his quest to provide us an entertaining & learned discussion of mathematicians & their tools (ruler/compass) used to arrive at Pi, a transcendental number: hence, circles cannot be squared. Beckmann dispenses nicely with Carl Theodore Heisel's claims to the contrary. The format of "The Golden Ratio" (story of Phi) by Mario Livio mimics Beckmann's book in its display of divagations (which in reality is a plus).

For those having interests in mathematics & history of numbers, etc., this book serves its purposes. Petr Beckmann disavows himself as historian or mathematician but this book would seem to prove otherwise. He knows & loves his numbers & respects the ingenious mathematicians responsible. The "History of Pi" is a delightful text to share the same shelf with Livio's "TGR: The Story of Phi". Its a steal.


An excellent example of proper historical writing   September 5, 2001
David J. Huber (New York, NY United States)
7 out of 8 found this review helpful

This is a great history of that enigmatic number. He begins with the first instance we can find of someone using math to determine circumference, and what value of pi they used, and how they likely found it. He then follows the development of pi throughout history, including both European and Asian developments. It is a fascinating story of coming ever closer to the real value of pi, and ever more ingenious methods of getting that closeness.

And contrary to the religious zealots who have reviewed so far, the history of pi, at least in Europe, cannot be told without making mention, and offering appropriate criticism, of the effect of the Catholic Church (and later, the Protestant church) on the development of pi, and of the development of science and mathematics in general. I very much appreciated that the author had the foresight, and the intelligence, to offer a history that is much richer than the majority of history texts I have ever read. Throwing away the old useless mantra of the "objective history", this author plunges headlong and offers his history with the full knowledge that it is impossible to offer a historical perspective that is free of bias. His bias is that of someone who wants to talk about the history of pi, and you can't do that without talking about who developed new ways of making closer numbers, and also of who strayed from the number through mathematical incompetence, or religious fervor that denies the mathematical truth in favor of "doctrinal correctness". The meddling, and also the support, of the Church is important historical data that need to be offered in a history text. Yes, he does come down very heavy handed on the church, and at times maybe a bit too much, but one can never be critical enough of a church that, for hundreds of years, burned scientists and mathematicians at the stake for declaring things that "weren't in accordance with Scripture". I mean, come on. He also delves into the political machinations that have thwarted and supported the development of mathematics, how some kings were supportive of advancing the science, how others were indifferent, how others were against it, and the effect those kings (or other leaders') wishes had on the advancement or retreat of science and mathematics.

It's an absolutely fascinating story. He does include a fair amount of mathematics, some of it quite developed, but the reader does not have to sift through any of it to get the history of the development of an accurate value for pi - the math can be completely skipped over, and the story is still there. His writing is lucid and clear, and he has a great way with making the story interesting and compelling so that the reader doesn't want to put the book down. And as I mentioned, I love this book because it very rightly includes the effect of religion and politics and economics on the development of something. I continue to be bored with history books that think they can talk about a whole period of history without having to mention the effect of religion, or the effect of science, or the effect of economics, or the effect of geography, etc. To all writers of history, especially those of you who insist on writing textbooks, please take this book as an example of how to write a **complete** history of something, and stop pretending that you don't have to talk about religion, economics, and culture at the same time, and that you can instead focus on a singularly political history. It just doesn't work.

If you enjoyed this book, I suggest you also read Galileo's Daughter. It will give you another good handle on the anti-science stance of the Church of that period, and it's also a compelling and wonderful read about an amazing man. With The Story of Pi and Galileo's Daughter, you will see how we of the Western world are amazingly lucky that the stranglehold of fear and suspicion and hatred that the Catholic Church held for so long was finally overthrown. We scientists/engineers, and the general population, would otherwise still have no science or math, and would continue to live in fear of coming into "heresy" and being burned alive. I also suggest reading "e: the story of a number", for the development of the counterpart of PI, which is also a well-written history, though it is strictly a focus on the math, and does little or nothing with the politics, religion, etc. of the development.


An antidote to today's hyper-sensitive history   March 22, 2000
23 out of 26 found this review helpful

My kind of book: A seemingly mundane subject that packs a punch. Those expecting an exhaustive mathematical treatise should remember that this is a HISTORY of pi, including the events and people that colored it. Beckmann is opinionated, and thankfully so! History is a story composed of characters that either advance or impede human progress, and Beckmann shines the spotlight on both, heaping scorn and reverence without regard to who's ox is being gored. In the process, he manages to annoy all the right groups (organized religion, fascists, communists) making him unpopular with some, but rare is the factual rebuttal to any of his charges. Indeed, the primary complaint seems not to be that he's wrong but that he's particularly unforgiving of history's morons. There's enough conceptual math and intriguing history to please both mathematicians and historians, particularly those tired of the politically correct drivel that so permeates popular science today. A truly great read.


Start down a new math path   March 24, 2006
Heather Arcand (Thermopolis, WY)
6 out of 6 found this review helpful

I picked this book up as a person more interested in "A History of. . . " than Pi. However after finishing this book, I immediatley went out and bought 3 more books about math. I was stunned to figure out that math was fascinating.

This book may not be comprehensive, and certainly the author shares his personal opinion about historical figures, but the name of the book isn't "A Comprehensive, Unbiased History of Pi". This book started me on a path from math phobe to math phile. Give it a try, your 7th grade teacherr was right math is cool!