Marc Chamberland
Teoksen Single Digits: In Praise of Small Numbers tekijä
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Lots of little snippets rather well presented. The topics change at the rate of about once every two pages. I didn't even get through the first chapter but found out that there was a straightforward non-recursive formula for every Fibonacci number. Most CS books don't even mention this, because they love recursion and memoizing so much. Skipping from chapter to chapter would be a perfectly reasonable strategy with a book arranged like this and probably a good deal more satisfying.
Tilastot
- Teokset
- 4
- Jäseniä
- 47
- Suosituimmuussija
- #330,643
- Arvio (tähdet)
- 3.5
- Kirja-arvosteluja
- 2
- ISBN:t
- 5
- Kielet
- 1
The idea is truly fun: A volume of mathematical facts and figures about only the smallest numbers -- one through nine. But there are two problems. First, it really doesn't confine itself to the numbers one through nine. And second, hardly anyone is going to follow all this.
I'm qualified to say that; I have a bachelor's degree in mathematics, and I had trouble understanding a lot of sections. In general, number theory -- which is what this is -- is about the most easy area of mathematics for non-mathematicians to grasp; anyone can understand, e.g., why the numbers three, six, and ten are triangular numbers, because you can set them out in the shape of a triangle. The fun is to realize that there is a formula for such numbers; the nth triangular number is 1+2+3+4+...+n (p. 71); another way to put this is that a number is triangular if and only if it is of the form n*(n+1)/2. Other simple situations you'll find here are things like the "pizza theorem" (which basically says that you can split a pizza into equal halves no matter how sloppy your cuts are), or the five Platonic Solids, or the four-color mapping problem, or the Erdós number (the original of the "six degrees of separation" phenomenon). And I love the "four hats" problem, guessing who is wearing which type of hat.
But this book goes far beyond such straightforward calculations. For example, the chapter on radioactive decay uses limits — pure calculus. There are infinite sequences, and series, and fairly advanced notations (e.g. Σ notation for extended sums, and Π notation for extended products). Or the chapter on the number nine has a section on "The Fifteen Theorem." For which you need matrix multiplication -- which I, at least, didn't meet until my second year of a college mathematics course.
Oh, and did you notice that number "Fifteen"? That's not between one and nine! Or, later in the chapter on nine, we get the Heegner Numbers, which are -3, -4, -7, -8, -11, -19, -43, -67, -163. So none of them are in the range 1-9, since they're negative, and even if you made them positive, five of the nine are larger than nine.
I repeat, I have a math degree -- and there were a quite a few items here that I couldn't understand. And there were a lot of items -- dozens at least -- that I only understood because I have a math degree. Some of these things could probably have been explained, if author Chamberland had explained rather than racing through his exposition as if he were being chased by cheetahs and trying to escape. But some truly needed college, or even graduate school, mathematical background. I'm pretty sure some of them aren't known even to the average mathematics Ph.D.
And if you want to look something up, the index is so short that it won't let you find anything -- neither triangular numbers nor the pizza theorem nor the four-color problem is in there, and while you can guess that the four-color problem is in the chapter on the number four, I don't know why the Pizza Theorem is under eight. Does it only work for eight pieces? The book doesn't say, and are we really supposed to remember that anyway?
Bottom line is that there are a lot of fun things in here, but there are so many areas of confusion that I think readers would be wise to skip this unless they're already deeply interested in fun math facts.… (lisätietoja)