A History of Pi

Rating:
Summary: How I want a drink, alcoholic of course...
Review: "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.

Rating:
Summary: A leisure read
Review: Buy this book if you are a math lover and are also interested in its history. Although It's not an serious math book that you can learn whole lot of math from, it does contain some mathematical derivations, formulas, proofs which can be skipped without destroying the coherency of the author's presentation.

Rating:
Summary: No Dry Pi History...
Review: I loved this book. I started reading on Thursday evening and finished on Sunday, enjoying almost every page.

It not only put the development of Pi into a world history context, it gave the author's opinions (well labeled) of who did what and what the effect was on not only the science and engineering communities, but the larger society(s).

I notice some reviewers see fault in this. Too bad. I guess they would rather have their Pi dry and eat it too.

For my own part, Mr. Beckman's 1974 3rd edition preface where he claims we were then entering a new age of scientific ignorance and anti-technology sentiment was RIGHT ON THE MARK! Consider what is happening in 2001 in California's energy industry. They build no new power plants for more than 10yrs, though demand is constantly rising, then I see housewives on TV claiming "isn't it suspicious that we suddenly run out of energy, and then the price skyrockets?" They start clamoring for price controls and even the governor publically discusses "taking over" the privately owned industry. This is a road to serfdom, and it starts with technology ignorance.

They understand neither technology nor free markets (where freedom is practiced and not an abstract thing) and the irony is that they have caused excess statistical deaths to now begin to occur while increasing the pollution of the environment over the intervening years of extending operation of older less efficient plants. But, by God, they do vote, don't they!

For those of you that don't get it, the history of Pi did not occur apart from the tolerance of society for scientists and technologists to practice their trade, and the historical intertwinning of technological intolerance and authoritarian regimes is actually the major theme of the book. Using the focused history of Pi to illustrate this theme strikes me as a not so subtle statement about the pervasiveness of the author's claim. The beauty of this metaphor to mathematicians should be the symmetrical knowledge of the pervasiveness of Pi in mathematical abstraction of all kinds.

I find much new material to think about in Mr. Beckman's book especially on Roman Civilation. I did not say I swallow his thesis whole, just that he has provoked me to think.

By way of full disclosure, I have university education(s) in electrical engineering and business administration. I would like to think I was pre-disposed towards freedom since before, but the truth is I had to learn to think first.

My advice, don't buy this book if you do not want to be provoked into thinking.

Regards to all, Roger Whatley

Rating:
Summary: Good for light reading, not fit for study
Review: I picked this book up as a sophomore in the mathematics department at the local university. I had for the previous two years been living and breathing only mathematics and was ready to scream. I was exhausted, frustrated, and quickly losing the love of mathematics that had fueled my progress thusfar.

Then I found this book at the bookstore. It was obviously nontechnical, but the last thing I wanted at the time was another text where it took days of concentration to finish a single chapter. Adding to this the fact that it was marked down to $, I couldn't pass on it.

The author has trouble distancing this work from his political, social, and intellectual views, and at times his paranoia that the Soviet Union would find a way to rule the world and destroy all works of science ever produced are annoying, and if this were deleted from the text it would probably be twenty pages shorter. But behind his rantings, we find an interesting presentation of the historical development of a number which keeps popping up in the most unlikely of places.

He highlights our progress in understanding the properties of pi and gives a sampling of the areas of mathematics, physics, and engineering where pi is often encountered.

Most importantly to me though, this book did not require the efforts of the college textbooks but gave an enjoyable and mildly addictive tour of classical mathematics. I believe that had I not found this text when I did I would have abandoned math.

Rating:
Summary: A Nice Insightful Book on Mathematics
Review: One of the reviewers complained about this book's continuous digressions. Well, you must know before reading this book that mathematicians were never great historians. Dr Beckmann is a professor of Electrical Engineering and this is more in the Physics side. This makes him potentially worse of a historian. But then would you please stop for a second and tell me what you want to know in a book about "Pi!"

I know I want to know almost anything there is about it. I want to know its origin, how people dealt with it in ancient days, and how people are dealing with it nowadays or in the past 100 year. Do not be mystified, for this number was known long long ago.

Then what is wrong with digressions? We want to know as much as possible, don't we? I saw that Dr Beckmann insights were all interesting. You would say, "Oh, yeah, another one of those geeky mathematicians." But I would only answer that I hate computers but read the section about applying the computer in computing new digits of this strange number.

This number appears in so many places in mathematics. The most famous is in the formula relating the circumference of the circle to the radius. And it appears in so many other sciences. It was the passion of so many amateur mathematicians to compete in the memorization of as many as a million digits after the decimal point.

Do you see why I decided to read the book? It is worth your time. Read it you too.

Rating:
Summary: small slice of pi, big helping of Beckmann
Review: 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!

Rating:
Summary: An analysis of the history of science via the example of Pi
Review: 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.

Rating:
Summary: A History of Pi
Review: This is a very interesting book, written about one of the most unusual numbers in math, irrational endless number, pi . The writter starts from the time of Greeks and beyond and nicely illustrates all the main points and other relevant topics besides pi. Multiple times does he refer to the wrongfullness of religion and how it set back science and math as well, and unfortunatly, sees communism as a bad religion, while not saying anything about the wrongfullness of capitalism, I mean come on, where's the fair play in the fact that top 5 richest people in USA have more money than 100 000 000 of the poorest ones? My point exactly, but overall, the author did a good job, even though it has quite a lot of personal bias in it.

Rating:
Summary: A journey through history, science and personalities
Review: This is more than a "book on mathematics". It is an engaging work, chock full of diagrams, charts and illustration, that serve to highlight the witty, erudite text. ALong the way we touch a variety of subjects, numerology, ancient Greece and Rome, professional jealousy, explorers, the Middle Ages and last, but not least, the seeimingly infinite ways in which people have tried to calculate the value of pi.

We start in neolithic times and advance to the Egyptians and Babylonians where he surmises on their attemtps to derive this important number. The book is arranged chronolgically and Beckmann attempts to portray the social and scientific conditions under which a particular theory was conceived. It is also the story of the greats of science, the giants of the mind - Archimedes, Euclid, Newton, Pascal and Euler (and thers).

Rating:
Summary: A journey through history, science and personalities
Review: This is more than a "book on mathematics". It is an engaging work, chock full of diagrams, charts and illustration, that serve to highlight the witty, erudite text. ALong the way we touch a variety of subjects, numerology, ancient Greece and Rome, professional jealousy, explorers, the Middle Ages and last, but not least, the seeimingly infinite ways in which people have tried to calculate the value of pi.

We start in neolithic times and advance to the Egyptians and Babylonians where he surmises on their attemtps to derive this important number. The book is arranged chronolgically and Beckmann attempts to portray the social and scientific conditions under which a particular theory was conceived. It is also the story of the greats of science, the giants of the mind - Archimedes, Euclid, Newton, Pascal and Euler (and thers).