Need a Christmas present for someone who likes interesting facts, with a mathematical flavour? Then this is the book. John D. Barrow is a mathematician/physicist at Cambridge University, who has given us a pot-pourri of intriguing things, with something for everyone who likes elementary physics, or is intrigued by various ways of counting.
In 100 short chapters, he covers plenty of ground, some of it in more than one way. He's at home with different schemes for deciding the winner of an election, and in one case shows how an obvious loser under a preferential voting scheme wins under a suitably contrived counting system. If you prefer purer knowledge, he gives a proof of Pythagoras's theorem devised by the US President James Garfield. And if you prefer more practical things, he gives a far more efficient method of boarding a plane than the one to which we are used.
Among my favourites is the chapter about why a tight-rope walker carries a long pole. I used to think it was because it lowered the centre of gravity, but not at all. As Barrow explains it's all to do with inertia, and in this context he gives the example of two balls of the same diameter and weight. In one the mass is evenly distributed, while the other is hollow and the mass is all concentrated near the surface. Which one rolls more easily down an incline? The first person I asked, who has a degree in mechanical engineering, got the wrong answer.
Here is another favourite, this one about pure physics, or even philosophy. If some modern theories of the universe are correct, we live not in a single universe, but a "multiverse". Some of the universes of this multiverse will contain beings more intelligent than us. While we can use computers to simulate things such as the weather, or the formation of galaxies, they might simulate a whole universe. How do we know we are not simply occupants in one of their simulations?