November 3, 2015 11:50:03 AM

3 November - "Math class is tough," Barbie used to say. She got silenced and no longer spouts on the issue, but it is only fair to remember that for lots of young people and adults, math is not easy. Even worse, it is not fun. This is a real shame. Mathematics reflects aspects of our existence with a mysterious fidelity. There are great mathematical ideas that can be contemplated and seen as beautiful by non-mathematicians, just as you don't have to write stories or be a professor of literature to enjoy a good novel. That's the appeal of *Math Geek: From Klein Bottles to Chaos Theory, a Guide to the Nerdiest Math Facts, Theorems, and Equations* (Adams Media) by Raphael Rosen. The author is not a mathematician, and that's all to the good. He is a journalist who has concentrated on writing about science. He says in his introduction, "I hope to show you that mathematics is not just a series of rote exercises performed in a classroom... I hope to convince you that mathematics is something built into the fabric of reality: a collection of shapes, patterns, numbers, arguments, and, well, little treasures." He has given a grab bag of brief mathematical snapshots of important or trivial parts of the world. Even pre-censorship Barbie could have fun with this book.

There are equations here, but not many. There is no need for an equation in the chapter on "Bell Choirs and Math," for instance, which has to do with change-ringing, or the ringing of church bells in all possible orders. If you have two bells, there are two arrangements, and if you have three, there are six; these are the permutations, changes in the order of ringing, and they skyrocket to huge numbers for steeples that have, say, eight bells. In change ringing, the order is varied in a planned way, so that every possible order eventually gets rung, with no repeats. The chapter on randomness has no equations. The internet requires the use of random numbers for all sorts of things, including commercial transactions, and it needs so much randomness that using physical generators like shuffled cards just won't do. Your computer can generate random numbers, and big ones, but a computer is a determinate gadget that follows whatever algorithm it is told. Computers generate pseudorandom numbers, which are good enough for, say, gamers, but not for high finance. Harvesting huge random numbers from teensy physical phenomena like radio static or quantum behavior ought to do.

There is a chapter on the famous Drake Equation, which is supposed to tell us how likely it is that we will be hearing from aliens from outer space. There is one equation in the chapter concerning miles per hour and why you should not tailgate. Many of the chapters do not even have numbers in them. This is one of the best parts of the book. Most people think mathematics means numbers, and of course that's a big part, but over and over here mathematics is shown to be patterns. Think of a golf ball and its pattern of dimples, for instance. There are recent golf balls that have hexagonal dimples, not circular ones, with the idea that the hexagons can cover more of the spherical surface. But why should golf balls have dimples at all? Is it not the case that smooth surfaces glide through the air more easily? Yes, but a little turbulence around the surface of the ball makes the air adhere a little better to the ball as it goes through, reducing the vortex and drag it makes behind it. Another practical question: Why are manhole covers round? (No, the answer is not "Because they cover round holes.") It's because if the covers were square or triangular, they could be dropped through the hole.

Now, Rosen does not go into further detail on circular manhole covers; he does not explain that the circle is the simplest example of a curve of constant width, and that covers formed with other such curves, such as the Reuleaux triangle, would also be forever undroppable. This illustrates the most attractive aspect of this book, which seen another way is a drawback. Each of the hundred chapters is very short, two or three pages sufficing for almost all of them. So the details may be lacking; Rosen introduces, for instance, the famous Tower of Hanoi puzzle, three pegs with disks on one of them, disks of different size stacked largest up to smallest. The task is to get the disks to another peg moving one at a time, without ever putting a larger disk on a smaller. Rosen explains how a large number of disks makes the number of moves incomprehensibly huge, but does not explain the simple iterative rules that always give the minimal solution. Many of the chapters here represent subjects that that have been more fully explored in weighty books of their own.

So *Math Geek* offers a taste of a wide array of entertaining subjects. What is the most efficient way to board an airplane (yes, this is a mathematical challenge)? How many clues have to be given for there to be only one solution to a Sudoku puzzle? Why does your checkout line seem slower than all the others? If you are in a rainstorm, do you get wetter if you walk or you run out of it? Why do we always think that raindrops are teardrop in shape, like in the cartoons, when they are much closer to spherical? How can some infinities be bigger than others? The scope here is wide, and the brief look at each subject is entertaining. This would be a superb book to give to a young person who is interested in math, but even better for one who is struggling with math and needs to see how all-encompassing and even fun it can be. You can count on any such person to find something interesting here, and to be able to do a few clicks on the computer and learn lots more in depth.