A History of Pi | 
 enlarge | Author: Petr Beckmann
Publisher: St. Martin's Griffin
Category: Book
List Price: $14.95
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Rating:  53 reviews
Sales Rank: 40708
Media: Paperback
Number Of Items: 1
Pages: 208
Shipping Weight (lbs): 0.4
Dimensions (in): 8.1 x 5.4 x 0.6
ISBN: 0312381859
Dewey Decimal Number: 512.924
EAN: 9780312381851
Publication Date: July 15, 1976
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Product Description
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.
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| Customer Reviews: Read 48 more reviews...
 Missed the subject June 14, 2008
1 out of 1 found this review helpful
"Missed the subject"
Although I am not a teacher, this is what I would have expected for grading, had I written anything to the subject at hand, and delivered this book.
I was interested to learn about the development of mathematics over the centuries. The title of book fit quite neatly into a collection of other books I have recently read. E.g. Number Theory and its History, E: the Story of a Number, the Story of SQRT(-1); and others. I expected to have explained the development of thinking and understanding of the fundamental numbers over the centuries. Instead I received collection of name calling, "Thugs", "Morons", "Idiots" and other names that simply have no place in a scientific book.
Dr. Beckmann used the book as a platform to express his emotions about religion and politics with an arrogance that does not fit the scholar.
Although some of the content is very informative about the subject at hand and mathematics and number theory in general, it is not sufficient to reward for having to go through the ranting.
I am disappointed and will not allow this book a place on my book shelf.
 Political commentary disguised as math history March 1, 2008
3 out of 4 found this review helpful
Despite its title, A History of Pi recounts more than the evolution of a geometric constant. In this case, moving beyond the core topic of the book turns out to be a bad thing. Yes, there is quite a bit of mathematical history, but the author simply uses that history as a platform to share his extremely biased view of government, religion, and society. At first it is distracting, then quickly becomes irritating. If you can make it past the first few chapters, you start to laugh at the off-topic rants. Once you reach that point, you can brush off the irrelevant bull and pay attention to the math history that motivated you to pick up the book in the first place.
For example, a chapter on Archimedes includes a figure with the following caption:
"Archimedes screw or helical pump. It is still used 23 centuries later by the Egyptian felahim, whose rulers think it more important to destroy Israel than to provide their people with modern irrigation."
Never mind that the chapter never once mentions the helical pump. Never mind that Egypt's position toward Israel has nothing to do with the history of pi. The author takes advantage of the most tenuous of links, leveraging a supposed compliment of the longevity of the ancient engineer's inventions and twisting it into a political statement, one which undermines the so-called compliment.
If I wanted a book on politics, I'd pick up a book on politics.
But the book isn't all bad. It does present the history of pi in the context of the societies which influenced its evolution. There are some mathematical insights I particularly appreciated. His explanation of the importance of proofs clicked for me, and his arguments were strengthened by a later discussion of the value of not-yet-proven theorems. The implications of the five Euclidian axioms was another highlight. Someone with more formal mathematical training than I have might find the mathematical treatise too light, but I thought it was just about the right length and the right level of detail. It isn't meant to be a scholarly work, so don't expect one.
But unfortunately the math is overshadowed by the hogwash. For a man that places so much importance on logic and proof in mathematics, it surprises me that he does not apply the same rigor to the political biases he espouses with such fervor. The poppycock can be partially excused once you realize the author lived in Czechoslovakia until he fled to the United States in the sixties; his life was shaken by Nazis and communists. His portrayal of WWII-era Germany shows how skewed the author's bias really is. While I do not support Nazi Germany in any way, his portrayal of the Germans as technologically inept, unable to come up with anything better than giant bells which use sound to kill, is unquestionably false. He condemns war, then arbitrarily selects acts of war and aggression and glorifies them. His absolute confidence in his positions makes no sense to me. Perhaps the inability to boil down history to a set of provable theorems has left the author with nothing to fall back on other than unjustified certainty in a misguided interpretation of history.
Most of the author's assertions make you roll your eyes, but there was one that I found particularly offensive. To demonstrate that a computer doesn't possess true intelligence, he compares the computer to an idiot savant. He says that both are "moron[s] whose total imbecility can often be quite exasperating." This is an ugly, insolent statement. It is clear that he believes the contemporary definition of idiot completely applies to an idiot savant. The author is the idiot here, placing absolute confidence in an opinion based on pure ignorance, just like many other of the author's assertions. I have had the honor of becoming acquainted with a so-called idiot savant, a man I am proud to call my friend. My friend clearly has some serious cognitive defects, and it is true that he doesn't understand how he comes up with answers to certain types of questions, but he is NOT an empty shell with no intelligence whatsoever. To focus solely on the unusual pieces of an idiot savant, both positive and negative, is to ignore the majority of who he is. The absence of certain skills lets the intelligence he does possess shine through, and helps you appreciate just how amazing human intelligence really is.
This book gets 4 stars for the parts that deal with the evolution of pi, but only 2 stars for making you wade through so much manure. Overall I give it three stars.
Great Book, Where It Sticks To The Topic September 6, 2007
5 out of 5 found this review helpful
First, let me say that this book is a good overview of a persistent mathematical problem; in this case, deriving the value of "pi," or the ratio between the diameter and circumference of a circle. The author begins at the beginning, by going over Stone Age "mathematics" and showing how and when it occurred to early humanity that this ratio existed. Second, Beckmann is very good when it comes to explaining the mathematics of pi and how it was analyzed historically in mathematical fashion. He also has a good handle on the primary-source material (i.e. historical treatments of pi), and can explain them in modern terms. All told, this makes it useful to someone who is new to the history of mathematics and wants to learn about one of its foremost problems.
Having said that, Beckmann clearly has some faults:
1. He frequently diverges into anti-communist rhetoric, not only tangentially, but at times when it's completely irrelevant and superfluous.
2. He views the past anachronistically; specifically his hatred of the Romans, and his contempt for Aristotle, are obvious.
He is technically correct on many of these scores; the Romans were, in fact, brutes compared to the Greeks, Carthaginians, etc. Aristotle also was also overrated. He is also correct in that, even in recent times, the Romans and Aristotle are given too much credit for things. None of that is in doubt.
What is troubling is that he arrives at these conclusions anachronistically. He see Aristotle as overrated, simply because Aristotle did not emphasize quantitative analysis over qualitative. But as a scientist he should realize that qualitative analysis has its place in the long process of learning. That Aristotle did not do what Beckmann personally (as a 20th century scientist) wished he had done, does not mean Aristotle contributed nothing useful to human knowledge.
Beckmann similarly laughs at other historical figures, implying that their lack of (modern-day) mathematical ability makes them contemptible. In his forward he even mentions that people took him to task for this, and appears amused at this critique. I'm not sure he understands the problem with anachronistic thinking, however. He clearly sees himself as "more clever" than figures of the past, as well as his colleagues who think he went too far in condemning the Romans and Aristotle; this shows a certain amount of hubris which is probably not penetrable.
His anti-communist rhetoric is, perhaps, more understandable, since he lived and studied under a communist regime, and later escaped from it. Even so, much of what he says about communism has no place at all in this book ... it's more or less irrelevant to the topic. Beckmann clearly could have written an "insider's" account of the faults and dangers of communist ideology, and perhaps he should have done so; but not here, in the guise of a treatise on pi.
To sum up: This is a valuable read, but only if you filter out Beckmann's anachronistic, personal biases.
A Delightful Read May 6, 2007
2 out of 2 found this review helpful
Beckmann's analysis of the history of pi is not the dry text that many would expect after hearing the title. The story that he lays out is not simply about the quest to figure out the number pi to as many decimal places as possible, but it is a comprehensive examination of the history of mathematics and science.
I admit, the mathematics in this book was beyond my knowledge. If you aren't already acquainted with geometry, trigonometry, complex algebra, and calculus, you might have some trouble keeping up with the proofs that pepper many of the pages. I assure you, the book is worth reading even if you skim over the mathematical proofs without understanding them. (As a side note, the only reason this book gets four stars is because the non-expert in math cannot read the book and understand the proofs that Beckmann provides).
There are many great chapters in this book that contain excellent expositions about various historical figures and their impacts. Beckmann delights in the exhaltation of great mathematical thinkers and in the putting down of what he thinks of as lesser minds (for example, Aristotle). In one part of the book he makes fun of Aristotle: "Aristotle used his lofty intellect to deduce that heavier bodies fall to the ground more rapidly; that men have more teeth than women; that the earth is the center of the universe; that heavenly bodies never change; and much more of such wisdom, for he was a very prolific writer." The chapters about Euclid, "The Roman Pest", Archimedes, Pascal, Newton, and Euler were all splendid, but I especially loved the chapter about the struggles between the superstitious church and the intellectual mathematicians and scientists.
Parts of this book were even amusing. Towards the end of the book, Beckmann recounts the stories of a few more modern "thinkers" who have claimed to "square the circle" (that is, who have found a value of pi that is rational). The author wastes no time to expose the weak-mindedness of these men, who were using values of pi that were used thousands of years earlier.
Overall, I loved the book and I intend to read it again in the future. If you're looking for a great read, pick this book up (but don't expect to be able to understand the math unless you are already an expert). When a friend told me to read this book four years ago (I finally got around to it), he told me that I would learn something that might save my life someday. I can only think of two possibilities: (1) Do not contradict the Bible by declaring your own beliefs to be more intellectual (because ignorant superstitious people often take matters into their own hands and torture/kill those who do), or (2) Do not waste your life trying to square the circle, because it cannot be done (as Michael Stifel put it: "Futile is the labor of those who fatigue themselves with calculations to square the circle."). Get a copy of this book and enjoy!
An interesting history - even when it gets off topic April 3, 2007
6 out of 6 found this review helpful
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.
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