From Zero to Infinity : What Makes Numbers Interesting

ACKNOWLEDGMENTS xi AUTHOR'S NOTE xii 0 ZERO Only a place-holder until finally recognized as first of the natural numbers. 1(14) 1 ONE A number that makes mathematics different from all the other sciences. 15(12) 2 TWO A primitive number system comes into its own with the electronic computer. 27(12) 3 THREE First among the odd numbers divisible only by themselves and one. 39(14) 4 FOUR Numbers multiplied by themselves provide beautifully difficult theorems. 53(14) 5 FIVE The pentagonal numbers turn up in the generating function of partitions. 67(10) 6 SIX Why has finding larger perfect numbers become increasingly important? 77(14) 7 SEVEN The problem of the prime-sided regular polygons has an unexpected answer. 91(14) 8 EIGHT Solving one problem about cubes leads to an even more difficult problem. 105(12) 9 NINE Add a third line to the two lines of the equals sign—and see what happens. 117(14) e EULER'S NUMBER An unnatural number answers the deepest question about natural numbers. 131(18) ALEPH-ZERO What set greater than the positive integers has the same number? 149(20) INDEX 169