Chapter 19

Ten Special Types of Numbers

IN THIS CHAPTER Associating numbers with shapes Characterizing numbers as perfect, narcissistic, and so on

Mathematicians classify numbers in many ways, much like psychologists (and gossipers) classify people: even or odd, positive or negative, rational or irrational, and so on. In this chapter, I show you even more ways to pigeonhole numbers by putting them into interesting groupings that make them special.

Triangular Numbers

Triangular numbers are numbers in the sequence 1, 3, 6, 10, 15, 21, 28, and so on (for more on sequences, see Chapter 16). You may have noticed that each term in the sequence is larger than the previous number by one more value than the previous difference between the terms. Say what? Okay, let me put that another way: To find the second term, you add 2 to the previous term. To find the third term, you add 3; add 4 for the fourth term, 5 for the fifth, and so on.

The formula for finding the nth triangular number is . Here’s how you use the formula to find the eighth triangular number (one more than the number 28 in the previous list): . The number 36 is 8 more than the number 28, which is 7 more than 21, and so on. ...

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