ABSTRACT
Folklore has it that when Napoleon Bonaparte, having been exiled to the island of Elba, set foot there, he exclaimed the words “Able was I ere I saw Elba.” Able he probably was, since he managed to escape from Elba within a year, and was soon in power again in France. Whether he knew English well enough to utter these words, and whether he truly said them are open to question. However, one thing is irrefutable: this sequence of letters (ABLEWASIEREISAWELBA) reads the same forward and backward. is sequence of letters exhibits a property called mirror symmetry, in this case about the letter R, the only letter that occurs once in the sentence. A sequence that exhibits mirror symmetry is called a palindrome. Palindromes have been the source of both delightful entertainment and serious exploration in a wide variety of domains for thousands of years. Mathematicians study palindromic numbers such as 37485658473.* Computer scientists analyze and generate palindromic sequences such as 1000001, as well as recursively palindromic sequences such as 1011101.† In a recursively palindromic sequence, the le and right halves of the sequence are also palindromic. us, in the latter sequence, the le and right halves given by 101 are also palindromic sequences but in the former sequence, the subsequences 100 and 001 are not. Writers and poets write books, stories, and poems that read the same forward or backward using, letters, words, or sentences as the units.‡ Artists and designers use decorative frieze patterns that are visual shape palindromes.§ e frieze patterns in Figure 30.1 are examples of geometric patterns that “read” the same from le to right and from right to le . In other words, each has re ection symmetry about a vertical line through the middle. Note that these patterns also enjoy mirror re ection about horizontal lines through their middles, and they are composed of pairs of adjacent units each of which also has local mirror vertical and horizontal mirror symmetries. e frieze at the bottom is also recursively palindromic at three levels of mirror re ection about vertical lines.
