Chapter 17

Ten Curious Types of Numbers

In This Chapter

arrow Shaping up with square, triangular, and cubic numbers

arrow Perfecting your understanding of perfect numbers

arrow Getting on friendly terms with amicable numbers

arrow Becoming one with prime numbers

Numbers seem to have personalities all their own. For example, even numbers are go-along numbers that break in half so you can carry them more conveniently. Odd numbers are more stubborn and don't break apart so easily. Powers of ten are big friendly numbers that are easy to add and multiply, whereas most other numbers are prickly and require special attention. In this chapter, I introduce you to some interesting types of numbers, with properties that other numbers don't share.

Square Numbers

When you multiply any number by itself, the result is a square number. For example,

  • 12 = 1 × 1 = 1
  • 22 = 2 × 2 = 4
  • 32 = 3 × 3 = 9
  • 42 = 4 × 4 = 16
  • 52 = 5 × 5 = 25

Therefore, the sequence of square numbers begins as follows:

1, 4, 9, 16, 25, . . .

To see why they're called square numbers, look at the arrangement of coins in squares in Figure 17-1.

Figure 17-1: ...

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