chapter  8
9 Pages

Number Patterns and Symmetries

WithMalcolm E Lines

Integers which read the same backwards and forwards are called palindromes. Some simple examples are 1,111, 12,321, and 1,397,931. Palindromes make up a rather small fraction of all numbers and they become progressively scarcer as the numbers get bigger. Thus, while every integer between 1 and 9 is necessarily palindromic in a trivial sort of way, only ten percent of the numbers between 10 and 1,000 are palindromes, and only one percent of those between 1,000 and 100,000 have this property. More generally, the probability of finding a palindromic number falls by a factor of ten every time we increase our number region of interest by a factor of 100. Nevertheless it is quite clear that we can easily make up a palindromic number of any length so that they can undoubtedly be found up to the largest numbers imaginable.