Okay, what do you get when you measure the circumference of a jack o lantern?
This is just one of the many little pleasantries that David Blatner has for readers in this most attractive little gem of an exploration of 3.1459.... There's also some pi poetry, some of which is not half bad. There are pi mnemonic devices, words strung out in prose or rhyme with the length of the individual letters to remind one of the string of pi digits. For example, "How I wish I could calculate pi." Or, "Sir, I bear a rhyme excelling/In mystic force and magic spelling...." In the same chapter, "Memorizing Pi" Blatner recalls some of the great mnemonic exploits of pi-dom, culminating in the incredible feat of one "Hiroyki Goto, who in February 1995 spent just over nine hours reciting 42,00 digits of pi from memory." (p. 111)
One of the questions I always had about pi was, Are the digits random? The number is irrational and transcendent so apparently the numbers never repeat. To me that always sounded like something close to a definition of a random sequence. Here I learned that in the first million digits, there are 99,959 zeros, 99,758, ones, 100,026 twos, 100,229 threes, 100,230 fours, 100,359 fives, 99,548 sixes, 99,800 sevens, 99,985 eights, and 100,106 nines. I would consider that distribution indistinguishable from random. Incidentally the first one million digits are printed in the book, albeit in such small type that you'll need a magnifying glass to make out the numbers.
But could the seeming randomness of the digits change as more and more places are calculated? Apparently not since "now, at over 51 billion digits on record, it appears that there's no statistically relevant difference..." between any of the numbers. (p. 73)
Blatner has a chapter on "The Circle Squarers." These guys are still hard at work trying to square the circle, something I have been told that not even God can do. Some of the tries are very amusing. People who work at trying to square the circle may be compared with those who work on building a perpetual motion machine.
Also interesting is how the present value of pi was arrived at over the centuries and the various ways people tried to get it as exact as possible. In the chapter on "The History of Pi," Blatner recalls the "earliest known record of the ratio" which "was written by an Egyptian scribe named Ahmes around 1650 BCE." He reckoned that pi equaled 256/81 or 3.16049. Blatner reports that the Romans used three and an eighth as close enough even though they knew three and a seventh was more accurate, simply because three and an eighth was easier to work with. (p. 20)
The book is filled with art work sometimes superimposed over the relentless march of the digits of pi in something like one-point type. There are many sidebars with interesting tidbits about pi and quotes from famous mathematicians. The book is fun to read and would make a nice little gift for the budding mathematician in your family or CIRCLE of friends.