on May 2, 2002
This book is not about Pi per se - it is a book about the history of mathematics, especially western math, with lots of opinions by the author, built around the example of Pi.
Readers who are interested in Pi would be disappointed, as they would expect a lot more material about Pi. I can see how the name of the book would mislead the buyers of this book in this way.
As a book about the history of math, I think it is a very good book - it covers the time span from the greeks to the modern era, focusing on western civilization (e.g. the far and middle east are mentioned very little), with chapters about the heavy weight mathematicians of the time. The author makes his opinions clearly and at some length, and I think he got quite a few good points.
The math is a bit difficult for a popular science book, and I get the impression the author just threw in a bit of math just as illustrations to main theme of the history of math and not in order to give the reader some insights and in-depth understanding.
So, if you want a book about the history of math in the west with the author's opinions and commentary, I recommend this book to you. But if you want a book about Pi, by all means skip this book.
on December 10, 1999
The thematic dissonance Dr. Beckmann serves up in this ostensible history of science treatise starts off very amusing, grows annoying towards the middle and ends up with you shopping for some other book on pi. As I finished the first chapter, I began to wonder whether other readers had noticed the bait-and-switch: a manuscript with seemingly scholarly intentions had been shanghaied by a cranky technocrat into service for a diatribe against everything from Aristotle to fascism.
The real let-down came several chapters further on. I largely agree with the political and historiographical assessments Dr. Beckmann preaches in his book: yes, Aristotle was a scientific dullard now lauded by posterity; yes, the Romans were mathematical morons who didn't even understand the hydrodynamics of their own aqueducts; yes, National Socialism was bad. I'll even concede that Dr. Beckmann's sardonic prose sometimes made the ubiquitous tangents an entertaining diversion. Still and all, what about pi? This is by far the tersest mathematical presentation of difficult ideas I have ever seen in a popular science text. Some of the explanations about mathematical reasoning are positively opaque --- but by the end you're grateful when there's any explanation at all.
I have to entertain the uncomfortable possibility that Dr. Beckmann omitted a thorough discussion of the technical points so that he could cram the proofs as well as his ideological agenda into a fixed number of words.
"A History of Pi", to give due credit, does touch on the major historical events in the study of this beautiful number (as long as you're prepared to forgive the limited coverage of computational developments, given the book's age). If an ad hoc mixture of political commentary, historical revisionism and dense geometric reasoning is what you're in the mood for, you've picked a winner. Otherwise you ought to look elsewhere. I learned much more about the history and role of pi from "E: The Story of a Number", by Eli Maor, than I did from "A History of Pi".
While this "history of Pi" presents a satisfactory accounting of the history of mathematics in a fairly enjoyable way, the author's tangents must relegate it to the b-string of math-oriented popular books. While I didn't find the lack of detailed proofs problematic, the compromise he attempts to find between proof-heavy math book and light popular book results in a rather schizophrenic treatment of some very interesting and relevant topics (such as continued fractions). He fails, too, to pursue the implications those useless digits of Pi have for our understanding of the universe, though perhaps when the book was written these implications weren't quite so obvious.
Many have described the opinion-heavy style of Dr. Beckmann; I only wish to add that his opinions are handed out in the classical Objectivist style. That is, they're in a tone meant to make the reader feel complicit in their sentiment and far above any reproach they might be dealing. For example, his complaints about the fledgling environmental movement neglect any facts and refer to activists as "frustrated housewives on messianic trips." This sort of dismissal out-of-hand is used on Aristotle, on the Romans, on the Soviets -- all based on few factual examples. While I *agree* with him on the great flaws of Aristotle (at least as a scientist and mathematician), on the Romans (though he apparently regards George Bernard Shaw's "Caesar and Cleopatra" as historically accurate enough from which to quote Julius Caesar), and on the Soviets (though Oppenheimer and Turing didn't get much fair treatment on "our" side of the Iron Curtain), I find this treatment distracting. He has other tricks to make the reader feel "smart" -- the epigraph for chapter 9 is the ever-popular "eppur si muove", but instead of citing it to Galileo, as is commonly done, he gives it to Giordano Bruno as a dying cry. While he acknowledges in the footnotes that there's not a single good reason to attribute it to Bruno, it's still the sort of gambit an author employs to send his reader quoting this new correction of popular fact to everyone he meets, feeling smugly superior.
I recommend the book, especially if you can get it inexpensively (it's terribly short). If ever you find yourself feeling superior when reading it, though, realize that you've fallen prey to Dr. Beckmann's little trap.
on March 21, 2000
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.
on February 13, 1997
Dr. Beckman was born in Czechoslovakia and lived for many years under Soviet rule. His experiences made him a particularly vehement and eloquent defender of individual freedom and that can be seen in "A History of PI".
This is not a dry recitation of the achievements made possible by the discovery of the relationship between a circle's circumference and its diameter. It contains such purely factual information but in a context which serves to show that free men can discover the truth, use it, and move all men -- free, unfree, rich, and poor -- forward; creating wealth, abundance, and leisure. The book also outlines those periods in history when freedom is crushed, the truth is lost, and men are dehumanized.
Finally, it cautions us that the struggle never ends. Indeed, in our own time a piece of legislation was submitted to the United States House of Representatives which sought to define PI as being equal to the integer value three [rather than 3.1415...].
Overall, the book is well written, readable, sometimes funny and sometimes deadly serious.
(The following is "as best as I can remember" and may contain some inaccuracies.)
Dr. Beckman was professor Emeritus of Electrical Engineering at The University of Colorado until his death in 1994. He published a number of books on his own which dealt with Engineering, Language, and Music (most notably "The Health Hazards of NOT Going Nuclear") and translated a number of works by Soviet Engineers and Scientists (most of whom were eventually destroyed by the system to which they were bound in servitude). He also produced "Access to Energy: A Pro-Technology, Pro-Free Enterprise Newsletter." He is survived by his Wife.
on September 7, 2001
This book is more of a chance for Petr Beckmann to give his personal opinions on historical regimes and figures than an exposition of the history of pi. That's not all bad - much of what he has to say is interesting and on target. I really enjoyed his skewering of Aristotle, the Romans, and the Spanish; as well as the homage to his heroes Archimedes, Newton, and Euler. But go in with your eyes open: pi is a sideline, not the main event.
The book also comes across as quite dated in two respects: First, Beckmann has a hard time writing more than a few pages without vehemently slamming the Soviet regime. Unfortunately, these diatribes border on McCarthyism. Second, the section on computer computation of pi is decades out of date.
I found the math somewhat terse and not particularly well explained. Some of the derivations were quite difficult to follow.
All in all, this is an interesting book, but not for anything to do with pi!
on April 2, 2007
It's very difficult to to summarize my opinion of this book. I did enjoy reading it, that much is true. But I can imagine it not being for everyone. The book has a strange mixture of math and history which I really enjoy, however the math is sometimes hard to follow and Beckmann often goes on long rambles in the book about his personal opinion about certain elements of history. I actually enjoyed those rambles, even if I didn't always agree; he has a talent for stating his complaints in a very humorous manner. I would suggest it to people but only those who are willing to think about mathematics in their free time and those willing to put up with rants about personal opinions. I did encounter some minor printing errors in my copy of the book, like the printing of "Chapter Four" at the top of one of the pages in Chapter Five. These did not, however, inhibit my reading in the least.
Beckmann is fascinated by history and it shows. He has a true enthusiasm for the subject and it makes the book more interesting to read. It does cause him to get off track at times, talking about things that have little relevance to pi, like the evolution of the calendar. These sections did not bother me as they were generally interesting and did not make the book that much longer (it is a fairly short book as it is, less than 200 pages); however, I can see some people getting irritated by this. Beckmann has a fairly conversational style of writing and this has much of the same result as the above. Like I said earlier, he makes no attempt to hide his opinions of various historical events and people, nor does he claim to be doing so: in the Preface he clearly states that he has never hesitated to "vent" his opinions. While this does mean that one must be critical of basing one's opinions off of his, I find it fairly amusing myself. For example, Beckmann spends basically the entire fifth chapter ranting about how the Romans are completely overrated and are basically just a bunch of thugs. I started wondering just what they had done to him until the last paragraph gave me the answer: the Romans killed Archimedes. It is also fairly clear that he absolutely detests Communism, fascism, and, for some reason, the UN. While I didn't always agree with his opinion, I found them amusing and they did not detract from the book.
The highest level of math in the book is basic calculus. It is not, however, necessary to completely understand the actually mathematics as long as one can follow the basics of what Beckmann is saying. Obviously, understanding what the mathematics he does are adds to the pleasure of the book but it is not necessary to remember more than basic algebra to really keep track of what is going on. What I'm trying to say is that it's very easy to skip all the math and still understand what is going on (more or less).
The very last section did bother me because it was all too prophetic and trying very hard to be significant. Beckmann envisions a time when "intelligent computers will make a better job of keeping peace among men and nations than men have ever been able to" (pg 189). I really don't think this is possible. A History of Pi is a very good little book but it is not for everyone. Besides being interested in the subject matter, it is also necessary to be able to find amusement in a well-stated opinion - even if it doesn't agree with one's own.
on July 7, 2003
"A History of Pi" is an amusing and informative romp through history with a most unlikely protagonist; a transcendental number that is know by the 16'th letter of the Greek alphabet, pi. Its pages contain historical developments, mathematical formulas, computational methods, and enormously entertaining facts, anecdotes, and trivia. It traces the understanding of this mere number from the ancients, into the dark ages, through the enlightenment, and on into the present, from stone tablet, to abacus, to digital computer. The list of notables whose legacies somehow impinge on 3.14159... include Euclid, Archimedes, Huygens, Pascal, Lambert, Leibniz, Newton, Halley, Euler, Lagrange, and Laplace, to name just a few.
If you haven't even a passing interest in mathematics, then this book will probably be an insufferable bore to you. Similarly, if your interest lies in the mathematics alone, not the surrounding folklore, history, or personalities, then the book will be nearly as insufferable. However, if you have any interest at all in mathematics along with its colorful history, then you will likely find Beckman's book to be an engrossing page-turner. To give you some idea of the range of topics that you will find in this book, here are several excerpts that I particularly enjoyed.
1) Beckman quotes the following episode, which is not directly tied to the number pi, but rather to the astounding calculating prodigies who dot the landscape of mathematics: "Truman Henry Safford (1836-1901) of Royalton, Vermont, could instantly extract the cube root of seven-digit numbers at the age of 10. At the same age, he was examined by the Reverend H. W. Adams, who asked him to square, in his head, the number 365,365,365,365,365,365. Thereupon, reports Dr. Adams, 'He flew around the room like a top, pulled his pantaloons over the tops of his boots, bit his hands, rolled his eyes in their sockets, sometimes smiling and talking, and then seeming to be in agony, until in not more than a minute, said he, 133,491,850,208,566,925,016,658,299,941,583,255!'"
2) Here is what Indiana legislators were up to in 1897: "The Indiana House of Representatives did consider and unanimously pass a bill that attempted to legislate the value of pi (a wrong value)...", which was "the equivalent of pi = 9.2376, ...the biggest overestimate of pi in the history of mathematics."
3) To illustrate the misplaced obsession of those who sought to compute pi to ever-increasing precision, Beckman relates the following quote: "Conceive a sphere constructed with the earth at his center, and imagine its surface to pass through Sirius, which is 8.8 light years distant from the earth [which is roughly 52,000,000,000,000 miles]. Then imagine this enormous sphere to be so packed with microbes that in every cubic millimeter millions of millions of these diminutive animalcula are present. Now conceive these microbes to the unpacked and so distributed singly along a straight line that every two microbes are as far distant from each other as Sirius from us, 8.8 light years. Conceive the long line thus fixed by all the microbes as the diameter of a circle, and imagine its circumference to be calculated by multiplying its diameter by pi to 100 decimal places. Then, in the case of a circle of this enormous magnitude even, the circumference so calculated would not vary from the real circumference by a millionth part of a millimeter. This example will suffice to show that the calculation of pi to 100 or 500 decimal places is wholly useless."
I should point out that the book contains more actual mathematics than I have found in virtually any other book that is intended (largely) for lay consumption. In its pages you will find numerous geometrical constructions, infinite series, calculus, and monstrous-looking continued fractions. Among the more pithy formulas you will find these:
pi / 2 = (2 * 2 * 4 * 4 * 6 * 6 * ...) / (3 * 3 * 5 * 5 * 7 * 7 * ...)
pi / 4 = 1 - 1/3 + 1/5 - 1/7 + ...
But all such formulas can be skipped over, or merely admired for their ingenuity, should the reader be unable, or unwilling, to grasp their entire meaning. I applaud Beckman for including such a panoply of mathematical formulas; it's hard to imagine doing the topic justice without them.
Oh, should you need to memorize pi to 15 significant digits (that is, 3.14159265358979), Beckman provides the following acronym: "How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics!" Enjoy.
on March 23, 2006
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!
on March 29, 2005
"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.