A History of Pi

by Petr Beckmann

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.

Genres: Mathematics, Science, History, Nonfiction, Popular Science, History Of Science, Stem

200 pages, Hardcover

First published January 1, 1970

Reviews

[Andrew Breslin · Rating 4 out of 5]

I received this book on March 14, during my annual pi day celebration. We had finished the pizza, but hadn’t gotten to the apple pie yet. We were listening to a special music mix for the occasion, including “Circle Dream,” by 10,000 maniacs, “Wagon Wheel,” by Old Crow Medicine Show and of course, “American Pie,” by Don Mclean. And while the pie was delicious, this made for an even tastier dessert.

What the world needs now are more opinionated and bellicose mathematicians, and I’m itching to pummel anyone who says otherwise. Everyone thinks mathematicians are a soporific lot who bring to their work all the passion and ardor of a three-toed sloth on barbiturates. But no! There are people out there who like math and haphazardly hurling invective at pretty much anyone who doesn’t have enough sense to duck out of the way.

Beckmann is one such calculating curmudgeon, never for a moment dissuaded to let fly with a litany of political opinions even while right in the middle of an equation. (“Now before we go leaping to the other side of that equals sign, let me tell you what I really think of the Soviet Union.“) He’s got an axis to grind. A chi(p) on his shoulder. A bone to pick (specifically: a radius).

You don’t have to love either math or getting into fur-flying cerebral brawls as much as Beckmann or myself in order to appreciate this book. But really: it doesn’t hurt. Don’t expect one of those popular math books that dumb it down and pretty it up to avoid offending or intimidating anyone. No punches are pulled here. Expect to be both offended and intimidated, and maybe a little confused. You might even be personally and directly insulted, and, what makes it worse: you won’t be sure.

Some of the math went sailing right over my head. Fortunately I do have enough sense to duck or I would have been smacked in the face with a dangerously pointy arctangent function, and we all know how much that would have sucked. Or maybe we don’t. The point is that you are almost certainly not going to understand all the individual mathematical details, but this doesn’t matter much. You’ll pick up the gist of it, and what a fascinating gist it is. The unsolicited rants about the Romans, the Catholic Church, and assorted megalomaniacal mathematicasters are just a delightfully fractious bonus.

I can hardly wait for March 14 to roll around again. I’m going to give this book to some worthy recipient, bringing its history with me, as well as this review, full circle.

[Joe Hilley · Rating 5 out of 5]

Great book. If you enjoy reading about the history of math, you'll enjoy this book. Even if you skip over the equations.

[Chad · Rating 3 out of 5]

The fact that it was written in 1971 adds a little bit of out-of-date flavor that makes "A History of Pi" a lot more amusing than it otherwise might have been.

As a history of pi, it kind of doesn't really work for a couple of reasons. First of all, its not really a history of pi. Its more like a history of mathematics in general. But even there, its far too anecdotal to serve as any real history lesson. Beckmann jumps and skips from one era to another giving you the lowdown on a random sampling of famous mathemeticians. The fact that he occasionally delves into the methods by which those mathemeticians were able to calculate pi with greater and greater accuracy over the years I guess justifies the book's title.

Secondly, Beckmann does absolutely nothing to make pi seem like the awesomly inpenetratable number that it is. The main reason I picked this up to read in the first place was because I recently read the chapter from Richard Preston's most recent book about the Chudnovsky brothers and their strange obsession with calculating the digits of pi. In that single chapter, Preston did a fascinating job of pulling you into the bizarre world of pi, and made me understand why a mathemetician could get lost in all those infinite, endless numbers. Petr Beckmann never really attempts to get into the philosophical implications of pi, and that left me a little wanting.

The third thing that bugged me was Beckmann's occasional lapses into opaque mathematical formulas. To his credit, he does include a helpful tip in his introduction:

"The reader who find the mathematics too difficult in some places is urged to do what the mathemeticians will do when he finds it too trivial: Skip it."

While I don't feel like I missed anything important in skipping over the many pages of equations, I am a little irked at being made to feel ignorant by the casual way in which Beckmann starts talking about things like the arcsin of the integrand.

Among these little problems, however, arises the "1971 Factor". This Factor manifests itself in a few amusing ways, not the least notably in the book's final chapter (apparently added in its third edition) about "The Computer Age". You can't help but laugh as Beckmann describes the BASIC programming language as "simple, but powerful". Its like basking in the delight of a five year old's amazement when you pull a quarter out of their ear. It's just so adorable.

The other amusing 1971 side effect is Beckmann's unmasked distate for those darned communists! Amid the sometimes dry historical accounts and the calculus equations and geometric theorems, the author just can't help himself and throws in several rather opinionated rants against those pesky Soviets. They made for some odd juxtapositions that brought a smile to my face every time they came up.

[By the way, Beckmann is a native of Prague, Czechoslovakia, and was forced to flee his home at a young age to escape the Nazis, so his personal distate for any sort of totalitarianism is quite understandable. It's just a weird tangent to wander into in the middle of a text on the history of mathematics.]

In the end, I didn't find "A History of Pi" to be a waste of my time. But it didn't quite live up to the mysterious awe inspired by the Preston artical that led me to pick it up in the first place.

[Elentarri · Rating 2 out of 5]

I listened to the audiobook while doing chores. This was probably not the best way to "read" a book that ended up having a vast quantity of equations and geometrical diagrams etc. A fair amount of the maths/geometry went over my head, but no doubt it would have helped if I had had the text in front of me, rather than listening to the audiobook.

Despite that, this book isn't so much a history of π, as an irreverent collection of historical factoids with some relevance to the advancement of mathematics (some of which are not accurate); mini-biographies of famous mathematicians; opinionated anecdotes; and the sometimes amusing rants in which the author attacks the Romans, the Church, institutionalized religion in general, imperialism in general, warmongers, communism and the Russians - woven throughout is the sequence of mathematical methods and proofs through time to determine the value of π with greater and greater accuracy. The original book and the next two editions were written in the 1970s during the cold war, providing a decidedly blunt and non-politically-correct vibe.

While the bits of history were interesting and the rants fairly amusing (ok! I agreed with some of them), this book ended up being disappointed in terms of learning more about the subject matter in a coherent fashion. The book was "ok" but not something I would recommend.

[Jeff · Rating 2 out of 5]

Dear Goodreads Admins:

Please rig your system so that the average star rating for this book is equal to the ratio of a circle's circumference to its diameter, rounded to three significant digits.

Thanks,
--jeff

P.S. I am still almost as ignorant about π as i was before reading this book. Disappointing.

[Satendra Deo · Rating 4 out of 5]

Easily readable for a mathematical book. Full of interesting anecdotes. A little light on Eastern mathematicians. Consider
1. Chinese - Lui Hui’s (3rd century) Algorithm - With this method Zu Chongzhi obtained the eight-digit result: 3.1415926 < π < 3.1415927, which held the world record for the most accurate value of π for 1200 years, https://en.wikipedia.org/wiki/Liu_Hui...

2. Japanese - Seki Takakazu (1642 – 1708 ) who knew Pi to 10 decimal places https://en.wikipedia.org/wiki/Seki_Ta...

3. Arabic - Refer Moustafa Mawaldi articleon the Arabic influence here http://www.muslimheritage.com/article...

4. Indians - have contributions from the greats Varahamihira, Brahmagupta, Sridhara , Aryabhatta and Madhava but one cannot go past Srinivasa Ramanujan whose fast (exponentially) converging infinite series of Pi opened the door for Digit Hunters to use computers to calculate Pi to trillions of decimal places. https://en.wikipedia.org/wiki/Sriniva...

SDe0 02/02/2018

[Jimmy Ele · Rating 5 out of 5]

Brilliantly outlined history of pi, but just like Charles Seife's "Zero The Biography of a Dangerous Idea", I am left wanting more. I want the Chinese, Mayan, and Indian history of pi. The Mayan history of pi was most likely burned by that one bishop, but the Chinese and Indian history I believe to be still in existence. Other than that, it was a thoroughly engrossing read and definitely nice to have read for my continuing Mathematics education.

[Charles · Rating 4 out of 5]

This book earns five stars for the explanations of the history how the knowledge of the ratio of the circumference of a circle to the diameter (π) progressed. The rating was reduced due to the inclusion of several snarky and otherwise irrelevant comments regarding politics and the actions of governments.
For reasons that have never been understood, π has received far more attention than all of the other constants. Even though other numbers, such as e, the base of the natural logarithms, are just as important in mathematics, they have not received the attention that π has. Beckmann does an excellent job of tracing the accuracy to which π is known as well as the many places where it has appeared as a component.
There is also a section describing some of the people convinced that they have squared the circle, despite it having been proven that it cannot be done. Underwood Dudley did the mathematical world a favor when he coined the phrase “Mathematical Cranks” to describe such people. There is also a section on the attempt by the Indiana State Legislature in 1897 to decree the value of pi. The bill unanimously passed the Indiana House of Representatives before it was permanently tabled.
The political viewpoint of the author is summarized well in the last paragraph of the content on the DJ describing the author.

“He also publishes a monthly pro-science, pro-technology, pro-free enterprise newsletter ‘Access to Energy,’ in which he promotes the viewpoint that clean energy can be made plentiful, but that access to it is blocked by government interference and environmental paranoia.”

Snippets of historical commentary similar to the tone of this passage are inserted throughout the book.
Pi has received more than its deserved amount of attention down through history, making its history extensive and long. Beckmann has developed a readable account of how knowledge of the number and its value has been explored by the greats and some not so greats.

[Jesse · Rating 2 out of 5]

The History of π is a fascinating work in the sense that it provides a narrative which frames for the reader, the development of this infamous mathematical constant’s calculation. The logical sequence of mathematical proofs as interwoven with the text is surely the strong point of the work. The weakness lies in the author’s multitude of obvious personal biases. Beckmann’s passionate political views quickly transform his attempt at a serious account in the history of science, to an ardent rant against all which he considers to be the root of societal evils. Consequently, his attack on Imperialism, the Church, and other institutions of power and orthodoxy should be expected, and they are not terribly callous. There are, however, some definite historical misrepresentations and oversights.
The biggest error in Beckmann’s thesis is his attempt to draw a divisive line between those who were engaged in so called “true” science and those who flirted with the occult. Recent studies have clearly indicated that many of the greatest scientific minds in Western history –including Newton, whom the author holds in such high esteem- did in fact experiment with occult practices.
Beside its flaws the book still stands as an interesting work of quasi-interdisciplinary scholarship.

[Dustin · Rating 3 out of 5]

In the first few pages, the author describes this book as being 'light on the math.' Well, you could have fooled me! Clearly, it is a book about math, and more than that, it is a book about a transcendental number, a constant that can NOT be written. So, starting from that point, you know that any math this *is* included is likely to be bizarre. Fair enough.

However, when the first few examples he gives of how the ancients found their values for pi are rendered into oh-so-simple differential calculus, it does not count as making the book math-lite to merely leave out the proof. Leave out the differential calculus, too! (Near as I can tell, the half-angle arctangent series are muy importanto to programming computers to figure out pi for us.)

However, the upshot to this book is that the author barely escaped from Soviet Russia, and so has ZERO tolerance for oppression in any of its forms. Therefor, his tangents tend to turn into rants, including my favorite part of the book, where he (successfully, IMHO) compares that paragon of western civilization, the Holy Roman Empire, with a few other empires: Napoleon's ill-fated French empire, Russia's ill-fated Soviet empire, and Nazi Germany's ill-fated Third Reich. He also pulls no punches when dealing with forces that have stifled or otherwise countermanded the course of scientific and mathematical progress, saving special vitriol for those who burned libraries. And to be clear, that was EVERYONE, at some point or another.

[Keith · Rating 4 out of 5]

When my oldest daughter was accepted to the North Carolina School of Science and Math (a college level high school for the smartest and nerdiest students in North Carolina), I went with her to orientation. At one of the sessions, the chairman of the math department came out and said, "This is what we teach in math here at NCSSM." Forty-five minutes later I leaned over to my daughter and said, "Have you understood anything in the last 45 minutes?" Saying that she had, I was baffled but reassured. My experience with that teacher is much the same as my experience with Petr Beckmann with this book. Beckmann relates some fascinating and rather opinionated stories about the history of mathematics and mathematicians while crossing my eyes with mind-numbing and incomprehensible (to me) formulae explaining how pi was calculated. Apparently one does not simply divide 22 by 7. Who knew? Beckmann comes down very hard on the Romans, who he equates with Nazi Germany (ouch) and relates some interesting stories about Archimedes, Newton, and other mathematicians whom I in my mathematical ignorance had never heard of. I skipped most of the real math (with the author's blessing, as he states in the preface), and stuck to the text which was satisfying for me in my own way. I'm sure someone well-versed in math would have gotten more out of it, but I can't say I was disappointed.

[Roberto Rigolin F Lopes · Rating 5 out of 5]

We are in 1970, Petr assumes that history of pi matches well with history of human civilization. After all, we are tool-wielding animals (from a quote in the book). Given a century (say between - 2000 and < 1970), our sophistication computing pi is related to scientific developments in that time window. And Petr dares to go through the centuries sharing his sharp opinion on civilization (he is hilarious sometimes). For example, some religious texts (say > 1) were happy with pi = 3. But, many years before, Archimedes (-212) wanted to know a “bit” more but other ancient Greeks couldn't handle irrationals/transcendentals (-322). Archimedes was the first to come up with an algorithm to compute pi to any desired precision. I laughed-out-loud with Petr comparing “Archimedean science” with “Aristotelian mambo-jambo” (he makes a reference Aristotle's book on Physics; which I read but don't recommend). He also points out that the Roman empire halted mathematical developments and it took a great intellect like Galileo (1564) to challenge Aristotelian ideas to start doing experiments. Then, comes Kepler, Newton, ... Euler, Laplace and computers. Takeaway: the ratio wit/page is higher than pi.

[Diego · Rating 3 out of 5]

Halfway through the book, the author writes that "the digits beyond the first few decimal places [of Pi] are of no practical scientific value. Four decimal places are sufficient for the design of the finest engines; ten decimal places would be sufficient to obtain the circumference of the earth within a fraction of an inch". And yet I find myself continuing reading through the rest of the book of how new methods to find more decimals places were discovered.
Although a little outdated in the last chapters, the underlying narrative of the book is a brief history of man, beginning in the stone age all the way through the "computer age" at the end of the decade of 1960's, with Pi as protagonist.
Curious is to grasp out how much progress we have done mathematically, but how much little progress we have done as human race. The author summarizes that throughout the history it has become fashionable to blame science and technology for the ills of society, and he writes in his last lines that perhaps the n-th generation of intelligent computers will make a better job of keeping peace among men and nations than men have ever been able to do.
We have failed so far.

[Donna Herrick · Rating 3 out of 5]

Why read a book about pi? Because pi is strange and interesting. Pi is the ratio of the circumference of a circle to it's diameter and area. So, if you want to figure out the number of servings in a family size pizza versus a medium or personal size pizza you need to understand and know the value of pi. For pizzas, the value of 3 is probably good enough. For sewing and planning building projects, an easy to remember and better approximation is 22/7.
The book describes the history of how people have created methods of calculating increasingly precise values of pi, now using computers it is up to millions of digits. In fact, the speed and accuracy 0f the calculation of pi is now used as a measure of the quality of microprocessors. My method of calculating the value of pi is to use the method of Archimedes, interpolating between inscribed and circumscribed polygons. But far more precise and rapid methods are derived from trigonometric functions that are described in the book. Unfortunately, those discussions were beyond what I remember of high school trigonometry and the book does not go into depth about how those formula were derived. On the other hand, the book is filled with dozens of funny asides about modern "circle-squarers", politicians, theologians and other crackpots.

[Davy Bennett · Rating 4 out of 5]

I liked the history portions of the book and tolerated the math parts.
Some interesting stuff, dude doesnt pull punches.
I like how he gives it to dictators like Frederic and Catherine the Great. I think he is a little hard on the Church.

[strategygamer22 · Rating 1 out of 5]

I picked this up at a library book sale for $0.50, interested to get another view of a topic that I already know quite a bit about. Wow, was I disappointed! The author states in the preface that he is neither a mathematician nor a historian, and it shows. Badly.

I questioned what this book was even supposed to be about multiple times while reading it. The author goes off on so many tangents and rants that he seemed desperate to NOT talk about pi. There's an entire chapter dedicated to developments of the calendar with no connection to pi. There's an entire chapter about how much the Roman Empire sucked and how the bloody barbarians brought nothing but death. This has nothing to do with the subject of the book. Not even remotely.

The mathematical sections are also explained poorly. I can do most of the math discussed with ease, but his way of explaining it made even me confused. It is overly explained for someone fluent in the topic, and too vague for someone not familiar with the topic. Overall, it benefits nobody.

The author also perpetuates the myth that science and religion are mortal enemies and have been from the beginning of time. Anytime progress was made by someone who was into "mumbo-jumbo" (his words), he dismissed them. Except for Isaac Newton, who the author clearly worships. A full chapter was dedicated to how Newton was the greatest scientist of all time and never did any wrong. Given Newton's odd religious beliefs and obsession with alchemy, the author should have dismissed him as quickly as he did Pascal. But this inconsistency is consistent throughout the book. This isn't a history book. It isn't a math book. It's just... pointless.

[Owen · Rating 3 out of 5]

This is the kind of book that Barnes & Noble publishes then practically gives away around Christmas as suggested stocking stuffers. I think that's how I ended up with it. Anyway, this book turned out to be much better than anticipated. It traces pi throughout history, going back to Babylonians and Egyptians and guessing how they might have arrived at their calculations. Practically every famous mathematician--Euclid, Descartes, Archimedes, Galileo Newton, Euler, etc--is discussed here, as pi has been a topic they've all either dabbled with or obsessed over.

Not only does the author trace pi's progress, he discusses times when pi (and by extension, math, science, and knowledge) made scant progress. These were periods of religious intolerance towards science, which the author despises and makes no effort to eliminate anti-religion bias. Okay, so it was published in the 70s, but regardless, the book got too preachy for me; at one point I think he asks, "How many Newtons have died in Viet Nam?" Several other jabs at Soviet labor camps are thrown in, often with limited context.

Pi in the computer age is a tacked-on last chapter in later editions. Even so, it's still two or three decades behind. Future editions should both expand on pi's use in modern math and update (or better, eliminate) the preachy Cold War side-notes.

[Papias · Rating 2 out of 5]

I'm enjoying this book; even with Beckmann's rants. But my problem is with his willful ignoring of facts, especially when you consider how little tolerance Beckmann has for good research. For example take this passage from the chapter Night:

In 1486, Torquemada sentenced the Spanish mathematician Valmes to be burned at the stake because Valmes had claimed to have found the solution of the quartic equation. It was the will of God, maintained the Grand Inquisitor of the Holy Office of the Inquisition Against Heretical Depravity, that such a solution was inaccessible to human understanding.

But if you read the endnote for this passage you find:

Depman. In fairness I must add that I have not found a reference to this event anywhere else, and Soviet books are unreliable where competitive religions are concerned.

Beckmann rips the Roman Civilization and the Catholic Church for two full chapters for lesser scholastic violations than this.

[Rod Innis · Rating 3 out of 5]

This book has a lot of the history of Pi - I can't type the symbol. It also has a lot of additional history of mathematics in general. I have read a number of such books. I just wish I could remember all that I have read!
There are some parts of this book where the math becomes too complicated for my not so mathematical mind, but the author does a pretty good job of simplifying quite a bit of it for the non-mathematician.
He does often show his bias against religion - particularly Christianity - particularly Catholicism especially in a time in history when they opposed good science for no good reason. Sometimes it is necessary to reject unbiblical scientific theories if they contradict biblical truth. He seems to reject Christianity as unscientific always. Science is right - religion is wrong! If you can get past his biases, you may enjoy this book. It is not a recent book. It was written in 1971. But since it deals with history, that only affects the most recent history.

[Mikko Karvonen · Rating 1 out of 5]

Fascinating subject - awful book.

While Beckman may know his mathematics and the story of pi, he lacks many other qualities necessary to write historical books. The writing is full of factual errors and problematic generalizations about non-mathematical things, as well as obnoxious and belittling attitude towards ancient cultures, their achivements and views of the world. A history books should not include off-hand remarks on how many historical mathematical documents arabs wiped their bottoms with or on priesthood of the time being more interested in religious non-sense than science.

It's a shame as I would have loved to read a well-written story about the history of pi. Now I grew so disgusted with author's attitude that I quit after reading about one fifth.

[David · Rating 4 out of 5]

Overall a good book. It's a bit dated, especially when the author talks about "modern" attempts to calculate pi on computers and how the current record is 500,000 digits (as of 2018, 2.7 trillion digits are known). There is some heavy math in the book, but it's not important that you understand it in order to enjoy the book.

My biggest complaint is how much of the book really isn't about pi. Entire chapters are about historical periods and other breakthroughs in mathematics with a spattering of "and during this time so-and-so calculated pi to 60 digits using Archimedes' method." I actually really enjoyed all of the other history in the book, it just didn't have anything to do with pi which is odd considering that the book is A History of Pi

[Jack · Rating 4 out of 5]

An interesting history

It’s hard to imagine that anyone could spend 220 pages talking about one number. It’s even harder to imagine how otherwise sane people would spend years trying to outdo each other in the number of decimal places they could achieve in calculating pi. That being said, the book turned out to be pretty entertaining. It has some interesting historical notes on great mathematicians and scholars as well as some righteous bashing of the church, the state, and the conquerors for suppression and destruction of scientific knowledge. Sadly, that still happens. Overall, I enjoyed the book.

[melydia · Rating 2 out of 5]

I like books about the history of math and numbers, but this one was a bit of a slog at times. Lots of equations. It also was strangely dated, what with the author's frequent scathing commentary on the USSR. He also feels a strong hatred for the Romans. Putting all that aside, there are some really interesting nuggets here and there, but in general I imagine this book would only appeal to the truly diehard number nerds.

[L. Scott · Rating 3 out of 5]

Entertaining, both for its handling of the topic, which is illuminating and entertaining in its own right when not jarringly interrupted by insufficiently introduced/notated mathematics, and for the bulk of the book, which vacillates between tangental to the topic and mere butterfly chasing and which contains much of the author's mockery of those who suffer from the Dunning-Kruger effect while often serving its own example of that. Some sort of Irony Tower (Dunning-Kruger-Turtle-Tower).

[Mark · Rating 3 out of 5]

I had no idea the history of a transcendental number could be so politicized! Wastes an entire chapter complaining about how the Romans were a bunch of pricks that he describes as a "thug state." Good for a giggle, and some good info about pi, but he holds nothing back when it comes to his Zionist agenda.

[Ryan Muzzey · Rating 3 out of 5]

Can’t give it a rating with six significant figures. Three is close enough, right? While I enjoyed reading the book, it veered away from the subject matter more than I would like. Some of the proofs were beyond me and might have been explained better. I still found it very interesting and learned quite a bit from it.

[Jim Conant · Rating 5 out of 5]

I first read this book when I was in middle school, maybe 6th or 7th grade, and it really captured my imagination. I saw many of the formulae in there as an exciting promise of math to be learned in the future. Reading the book a second time now, I'm bemused by the author's many strong opinions. There are few places where you'll find Aristotle dismissed as a twit, but it's refreshing for sure.

[Jim]

unsure if this is the Pi book I read ten years ago?


History records the names of royal bastards, but cannot tell us the origin of wheat. JEAN HENRI FABRE (1823-1915) is a great quote which starts the book.

also in my book notes I am trying to save words that are new to me .

[Robert · Rating 5 out of 5]

Interesting presentation about PI, and a devastating critique of how first Rome then the Roman Catholic Church postponed progress for nearly two millennia.

Just technical enough to tell the story, an enjoyable and fast read.

[Uday Desai · Rating 5 out of 5]

Excellent book!! Petr Beckmann made this history so interesting, if you like mathematics or just curious, you will be able to enjoy it.