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Petr Beckmann

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A History of Pi Paperback – July 15 1976

by Petr Beckmann (Author)

4.4 278 ratings

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The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

Review

“A pure delight . . . Entirely offbeat, which gives it its charm.” ―The Denver Post

“A very readable account.” ―Science

“A cheerful work.” ―Scientific American

From the Back Cover

The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress and also when it did not, because science was being stifled by militarism or religious fanaticism. The mathematical level of this book is flexible, and there is plenty for readers of all ages and interests.

About the Author

Petr Beckmann was born in Prague, Czechoslovakia, in 1924. Until 1963, he worked as a research scientist for the Czechoslovak Academy of Sciences, when he was invited as a Visiting Professor to the University of Colorado, where he decided to stay permanently as professor of electrical engineering. He has authored books including The History of Pi and more than fifty scientific papers, mostly on probability theory and electromagnetic wave propagation.

ISBN-10

9780312381851
ISBN-13

978-0312381851
Edition

19th ed.
Publication date

July 15 1976
Language

English
Dimensions

13.97 x 1.32 x 20.96 cm
Print length

208 pages
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Product details

ASIN ‏ : ‎ 0312381859
Publisher ‏ : ‎ St. Martin's Griffin; 19th ed. edition (July 15 1976)
Language ‏ : ‎ English
Paperback ‏ : ‎ 208 pages
ISBN-10 ‏ : ‎ 9780312381851
ISBN-13 ‏ : ‎ 978-0312381851
Item weight ‏ : ‎ 1.05 kg
Dimensions ‏ : ‎ 13.97 x 1.32 x 20.96 cm

Best Sellers Rank: #332,945 in Books (See Top 100 in Books)
- #71 in Number Theory (Books)
- #85 in Mathematics Reference
- #215 in Mathematics Study & Teaching

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4.4 278 ratings

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Shahab Mahvi

A comprehensive history for both amateur and professional mathematicians

Reviewed in Canada on April 8, 2023

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The author's writing style and the way he introduced topics are both good. I could not stop reading to know what will be the next chapter. I was totally aware of many of the items in the history of Pi but this book was one of a kind. The price is good too. Highly recommended.

Reviewed in Canada on October 19, 2011

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Although I only read the first 3 chapters of this book, I found it quite interesting. It traces the origins of pi through many civilizations and mathematicians, and is only occasionally fettered by the mathematics.

2 people found this helpful

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Neil

Five Stars

Reviewed in Canada on November 17, 2015

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Simply excellent!

One person found this helpful

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Gord McKenna

A lovely read for all

Reviewed in Canada on August 8, 2010

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Wow, nicely written, an entertaining historic story, just the right amount of math, this book has set the tone about people writing about mathematics. Highly recommended.

2 people found this helpful

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Paul S.

A great read

Reviewed in Canada on January 10, 2018

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Great book on an intriguing subject

One person found this helpful

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David J. Huber

An excellent example of proper historical writing

Reviewed in Canada on September 5, 2001

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.

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James Arvo

How I want a drink, alcoholic of course...

Reviewed in Canada on July 8, 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.

7 people found this helpful

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Randolph Eck

An interesting story of PI

Reviewed in the United States on April 25, 2021

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It seems that by 2000 BCE, the significance of PI was appreciated, and a rough approximation was known. It appears that the Babylonians and the Egyptians were aware of its existence and significance. The symbol for PI was not generally used until the 18th century CE. Incidentally, the equal sign did not come into general use until the 16th century. Early on, it was the priests in Babylon, Egypt, and Maya societies that were the learned ones – the astronomers, calendar makers, and timekeepers. Interestingly, the Mayans “could out-calculate the Egyptians, the Babylonians, the Greeks, and all Europeans up to the Renaissance,” with their vigesimal, positional notation system.

An entire chapter is spent on the early Greeks and their contributions. The philosopher Antiphon enunciated the “principle of exhaustion,” which had a profound influence on the quest to determine a more accurate value of PI. We also learn of the contributions of Hippocrates and his use of reductio ad absurdum (reduction to the absurd). There is also the contributions of Hippias of Elis, Eratosthenes, and Euclid. Following the Greeks were the Romans, whom the author characterizes as thugs. Their contribution to science, according to the author, was “mostly limited to butchering antiquity’s greatest mathematician, burning the Library of Alexandria, and slowly stifling the sciences that flourished in the colonies of their Empire.” It was a Roman soldier that killed the great thinker Archimedes. How sad.

Born in 287 BCE, is the great Archimedes of Syracuse. He was the first to provide a method of calculating PI to any desired degree of accuracy. His polygonal method remained unsurpassed until 19 centuries later. I wanted to mention here, that the author provides a bit of mathematical detail throughout this chapter and the rest of the book, which one might find difficult to follow. Fortunately, it is not necessary to understand the details in order to appreciate the developments of these great thinkers.

We segue now into the middle ages. Unfortunately, we see no significant progress in the method of determining PI until Viète (1540-1603). Other notables that contributed to the value of PI were Fibonacci (1180-1250), and Christiaan Huygens (1629-1693). Unfortunately, throughout history we have too many instances of the destruction of scientific thought. The torch of Alexandria was extinguished by militaristic Rome, the intellectual life in Babylon was wiped out by the militaristic Assyrians, and the golden age of Muslim science was stifled by the militaristic Turks, according to the author. We have similar stories from India and China.

By the time of the Renaissance, we see ever increasing accuracy of the numerical value of this constant. Trigonometric functions and logarithms have come to the rescue. At this time, Viète was the first to represent PI by an analytical expression of an infinite sequence of algebraic operations. In time, we see people trying to calculate PI to an ever-increasing number of decimal places. This is interesting since the digits beyond the first few decimal places are of no practical scientific value. We learn of further developments revolving around PI with Leibniz, Newton, and the development of calculus. Interestingly, it was in Newton’s lifetime that the circle ratio was first denoted by PI. Later, Euler developed formulas for PI by the truckload. The author presents a bit of math in these chapters showing us just how some of these formulas were conceived, but don’t worry, you can understand the text without comprehending all the derivations. In the 1700’s, the irrationality of PI was established by Johann Lambert and Adrien-Marie Legendre. By 1840, the existence of transcendental numbers is proven, and we find out that PI is just such a number, this being proven by Lindemann in 1882. This had important implications as it showed that the possibility of squaring the circle by Euclidean construction was impossible – not that that stopped people from trying.

The author concludes saying, “The history of PI is only a small part of the history of mathematics, which itself is but a mirror of the history of man. That history is full of patterns and tendencies whose frequency and similarity are too striking to be dismissed as accidental. Like the laws of quantum mechanics, and in the final analysis, of all nature, the laws of history are evidently statistical in character.” The conclusion to an excellent book, I thought.

6 people found this helpful

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Excelente

Reviewed in Mexico on December 24, 2019

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Interesante conocer la historia por la que a pasado el número pi, su calculo a través del tiempo, la obsesión del hombre para encontrar su exactitud.

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tootoot

An interesting story.

Reviewed in the United Kingdom on November 12, 2019

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This is a fascinating insight into the history of this strange number. Starting with how the ancients worked out how to use Pi to computers calculating Pi to huge numbers of decimal places covering the many ways developed to calculate Pi down the centuries all explained in an easy to understand way. The book is not right up to date as it was written many years ago, but that does not detract from it's value.
The author also has a sense of humour that shows itself in the many digs he has at some of he famous names of the past who he feels were perhaps not as clever as we thought!

One person found this helpful

shivali

Wonderful book for math lovers.

Reviewed in India on July 8, 2019

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Wonderful book for math lovers.

One person found this helpful

Jean-Luc

Descriptif et rigoureux

Reviewed in France on January 1, 2019

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Parmi tous les ouvrages sur PI, celui-ci est clairement le meilleur et le plus complet que j'aie lu jusqu’à présent. Il est à la fois historique et mathématique.

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