A History of Pi | 
|  | | | Title: | A History of Pi | | Author: | Petr Beckmann | | Publisher: | St. Martin's Griffin | | Type: | Book / Paperback | | Publication Date: | 15 July, 1976 | | ISBN / ISBN-13: | 0312381859 / 9780312381851 | | List Price: | $14.95 | | You Save: | $4.78 | | Amazon Price: | $10.17 | |
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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:
• Great Book, Where It Sticks To The Topic 06 September, 2007
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.
- Reviewed by customer ID: A3GANIWUW6UPZR
• Political Commentary Disguised As Math History 01 March, 2008
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.
- Reviewed by customer ID: A3NWYWN8IIOSI1
• Beckmann -- Yet Another Professor Making Uc Boulder Look Bad 12 September, 2008
Beckmann, a former professor at UC Boulder, should've known better. Of course, what should we expect from someone who spent most of his life trying to debunk the theory of relativity?
As many of the reviews have stated, Beckmann spends a lot of time discussing his pet political opinions and not a lot of time actually discussing pi. His tone is horrible and most of his asides aren't only unrelated to his arguments, but completely unsupported. Although I agreed with a lot of his opinions, they had no place in a book about the history of mathematics.
If you're looking for a general history on mathematics with a lot of hyperliberal rants, then this might be the book for you.
- Reviewed by customer ID: A1QL6JFAENARXT
• Missed The Subject 14 June, 2008
"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.
- Reviewed by customer ID: A25W8WIR2N3EJS
• A History Of Pi Review 15 October, 2008
I find the book to be an interesting and detailed read. I'm a mathematics major, however, I feel that my sister who hates mathematics could follow and possibly even enjoy.
I also like the author's point of view on some of the material, i.e. a quote from Bechmann on Archimedes' famous 'Water-Screw', "It is still used 23 centuries later by the Egyptian felahin , whose rulers think it more important to destroy Israel then to provide their people with modern irrigation."
This book doesn't only include interesting history of Pi, it includes topics also related to it as well as the mathematicians involved and the importance of Pi.
- Reviewed by customer ID: A1GPA955P9M4UA
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