Strange Curves, CouSnting Rabbits and other Mathematical Explorationsis an excellent popular math book for the right audience. I had a lot of fun reading it, and will probably re-read at some point.
What is the audience for Strange Curves, Counting Rabbits and other Mathematical Explorations?
This is a book of recreational mathematics, but it is relatively serious. Several of the chapters have some calculus, one has a bit of simple matrix algebra. So, if you are reading this on your own, it’s probably best if you had at least one course in calculus at some point – even if you don’t remember it very well. So, that’s one audience.
Another audience for Strange Curves, Counting Rabbits, and other Mathematical Explorations is teachers of advanced high school students who want some ‘enrichment activities’. Each chapter is pretty much self-contained, and would make for one or more good discussions about interesting mathematical topics.
How can you read Strange Curves, Counting Rabbits and other Mathematical Explorations?
I think there are two main ways to read this book, and they correspond to two ways of looking at math. One is a “how-to” approach, in which you are trying to learn to do more types of math. The other is a “look at this” approach, in which you are just enjoying looking at some beautiful math. You could make an analogy with art – you can go to a museum and look at paintings, or you can take an art class and learn to paint.
Of course, these aren’t totally separate – you don’t learn to paint without looking at art – but you can certainly go to a museum without knowing how to paint. Similarly here. You can use this book to learn to DO math, or you can use it as a mathematics appreciation course.
What topics are covered in Strange Curves, Counting Rabbits and other Mathematical Explorations?
There are ten chapters:
1. Shannon’s Free Lunch, which is about codes that, unlike the usual code, attempt to make communication clearer and less error-prone. Did you know, for instance, that the ISBN numbers on all books are not just randomly assigned? Rather, they can be used for error checking, so that if you give someone the wrong ISBN (or they transcribe your request incorrectly) it is very unlikely that the wrong number corresponds to a real book? Even more, if you get one digit wrong, it is likely that the person reading the number can figure out which number it is, and what the right one is.
2. Counting dots, which covers Pick’s Theorem, a charming bit of geometry.
3. Fermat’s little theorem and infinite decimals Fermat’s little theorem states:
If n is a whole number and p is a prime, then np– n is divisible by p.
and you’ll learn more about it in this chapter
4. Strange Curves covers some very odd curves, like the Peano curve which, even though it is of infinitessimal thickness, covers an entire plane, and fractals.
5. Shared Birthdays, Normal Bells discusses the “birthday problem” (i.e. suppose there are 23 people in a room, and each writes his or her birthday (month and day, not year) on a piece of paper, what are the odds that two match?) and also the famous Normal probability curve (the “bell shaped curve”).
6. Stirling Works is about one of the most remarkable formulas in math:
n! is approximately equal to (2*pi).5 e-nnn+1/2
where n! is the factorial, e.g. 3! = 3*2*1
Amazing! What is pi doing in there?
7. Spare Change, Pools of Blood is about how to detect counterfeit coins with only a few weighings, and how to find out which (if any) patient in a large group has a disease with as few blood tests as possible
8. Fibonacci’s Rabbits Revisited is about the Fibonacci numbers, which start
1 1 2 3 5 8 13 …..
that is, with two 1’s at the beginning and then each number is the sum of the previous two, and some variations such as Lucas numbers, which are similar but start with 1 3
1 3 4 7 11 18 .,….
and also about continued fractions
9. Chasing the Curve. Many people in the audience for this book will have heard about Taylor series, which are used to approximate functions. But they don’t work very well for some functions. One method that works better in some cases is Pade approximations, which use rational functions to approximate a curve.
10. Rational and Irrationaldiscusses how we can determine if a given number is rational or irrational.
The author of Strange Curves, Counting Rabbits and other Mathematical Explorations is Keith Ball, He is a professor of mathematics at University College, London, and gives popular lectures on mathematics, as well as authoring graduate level books on math.