This is another of the books that I scored at the most recent OpenBooks “box sale” (I really did very well with that, despite splitting the box with my daughters and one of their BFFs!). Petr Beckmann's A History of PI is well known, having been kicking around since 1971, but possibly more for its reputation of being somewhat cantankerous than for its research.
Beckmann has an interesting biography, having fled his native Czechoslovakia ahead of the Nazi invasion, his family spending the war years in the U.K., where he flew with the R.A.F. In a Czech squadron. After the war he returned to Czechoslovakia (now on the other side of “the iron curtain”) and completed a doctorate in Electrical Engineering. In 1963 he managed to get invited to join the faculty of University of Colorado and moved to the U.S., became acquainted with Ayn Rand, and functioned as a contributing editor of an Objectivist publication. I usually wouldn't background an author like this, but there are aspects of his writing which make considerably more sense in context. Two things constantly draw his ire, “militaristic” states (be they Rome, the Nazis, or the Soviets), and Religion. You might well ask, “What do those have to do with π?” to which the answer is “not all that much, really” (well, except for Fundies who want to make π equal something other than what it does, based on some vague biblical twaddle in 1 Kings VII.23). However, this does not stop Dr. Beckmann from constantly firing off broadsides at his favorite targets while tracking the historical development of π.
This is one of those books which would have been vastly improved by involving a real editor … while not so much as in the cliché cases of Doctors and Lawyers who act that role for themselves, this is a case where “being his own editor” made the resulting book a far, far weaker venture than might have been the case with some less reactive voice saying “no” where necessary!
While reading this, it occurred to me that Dr. Beckmann was “a man before his time”, as the chapters in this book would have been much more effective as posts to a website ... frankly, on some levels, it substantially reminded of parts of Richard C. Hoagland's site ... and Beckmann could have ranted continuously on the web, were he not under the constraints of putting ink on paper. The book certainly reads like a “fringe” site, where the author clearly knows quite a bit about his subject, but is taking that knowledge into justifiably uncharted territory.
The “meat” of the book, however, is pretty solid. He starts with a look at human culture, and posits a “belt” where agriculture developed and allowed people to have specialized roles, including those involving numbers. He looks at how π was likely approximated by various cultures, the Babylonians, the Egyptians, the Mayans, ancient Chinese, etc. with only the occasional predictable (and fully justified) slams at religion where it intentionally eradicated the amassed knowledge of entire cultures (as with the Maya, Aztecs, and Incas).
He then moves to the Greeks, and discusses several leading lights, some well known, some less so. Here too he is not shy in expressing his dislike of some (Aristotle) and his extreme admiration of other (Archimedes). However, when the discussion rolls around to Rome, he lets fly:
He constantly refers to the Romans (and the likes of Caesar) as “thugs” and frequently draws parallels to the Soviets.Rome was not the first state of organized gangsterdom, nor was it the last, but it was the only one that managed to bamboozle posterity into an almost universal admiration. … They have been led to believe that the Romans had attained an advanced level in the sciences, the arts, law, architecture, engineering, and everything else.
It is my opinion that the alleged Roman achievements are largely a myth; and I feel it is time for this myth to be debunked a little. What the Romans excelled in was bullying, bludgeoning, butchering, and blood baths.
Needless to say, moving forward into The Dark Ages, he doesn't become any kinder to the Church of Rome, which made a habit of torturing and murdering practitioners of Science as though they were toiling in “Dark Arts”.
If there is one thing this book is good for, it's a survey of prominent mathematicians over the years. Much of the structure of the book is looking at how various of these had addressed π and moved forward with the precision of its determination as well as methods for its calculation. I was, frankly, surprised at how many different ways one could come up with π, and how many people had made strenuous efforts to push forward the number of known places (a graphic at the end of the book reproduces a computer print-out of the first 10,000 decimal places of π).
The author also spins out assorted mathematical trivia that one might not know (I didn't) like the Greek letter “π” was not used until fairly late in history, and was derived from “periphery”, and that “sine” in the measurements of angles, etc., came from a mis-translation where a Hindu term had been translated into Arabic, and the Latin translation from that assumed a wrong vowel amid the written consonants, and came up with “bay”, which then got made into “sinus” … having no relation to the original term which meant something along the line of “half-chord”.
The book is also quite full with chunks of fairly advanced math. I'm a bit of an “untutored” math fan, and was lost from the get-go here. However, Beckmann suggests that the non-specialist simply ignore those parts, and I (like most, I assume) did so.
Amazingly, A History of PI is still in print 40 years on, with a paperback edition that the on-line guys have at over a third off, and under ten bucks, however the used vendors have “like new” copies of the hardcover edition that I have for as little as one cent (plus shipping, of course), so this could be had for cheap. I'm torn on this … I'm glad to have read this as a historical over-view, but irritated at it at the same time (and the math just flew by over my head) … if it sounds like “your thing”, by all means pick up a copy, but this sure isn't an “all and sundry” recommendation!