When I was a kid one of my favorite books was George Gamow’s One Two Three . . . Infinity: Facts and Speculations of Science. (It’s a pity that the current edition has such a crappy cover. Here’s the cover to the copy I own, which is much cooler looking). This book taught me about huge numbers, infinity, and the fourth dimension. I loved Gamow’s hand-drawn illustrations, too. If you don’t have this book, I suspect you will enjoy it.
Professor Stewart’s Incredible Numbers, by Ian Stewart, reminds me of One Two Three . . . Infinity. It’s missing the charming hand-drawn illustrations, but it has many of the same topics in Gamow’s book (like the Towers of Hanoi, and the Four Color Map Theory), plus quite a few other fun number-related items that Gamow didn’t cover, such as fractals, the Birthday Paradox, and the Sausage Conjecture.
When I told my 12-year-old about the Four Color Map Theory, she immediately went to work with colored pencils and paper to prove me wrong. I can’t find the fantastically complex maps she came up with, but if I locate them, I’ll post them here. She eventually came up with an intuitive understanding of why any map you draw only needs four colors to ensure no two bordering shapes have the same color.
UPDATE: I found Jane’s maps:
