1. PALINDROMES

2. A palindrome is a number, a word, a phrase, a sentence, even a book or two that reads the same backwards and forwards, ignoring punctuation. Legend has it that the first thing Adam said when he met Eve was, “Madam, I’m Adam” to which she replied “Eve” while pointing to herself. Notice both of them are palindromes. Palindromes have probably not been around that long but they do date back more than 2000 years. The first known reference to one was made by Sotades of Maronea around 275 BC.

3. Since their discovery people of all languages have played with letters to make palindromes of various lengths. Some of the more thought- provoking ones in English are: “A man, a plan, a canal, Panama”, “Able was I, ere I saw Elba”, and “Rats live on no evil star.” There is even a palindromic book of 2002 words written by Nick Montfort and William Gillespie. I did find a reference to another one but was unable to find a title or author. As fascinating as these verbal palindromes are, I find the numeric ones of even more interest.

4. Numeric palindromes have been around just as long as verbal ones. But unlike those made with language, it is fairly simple to make a numeric palindrome. You start with any 2 digit number. Reverse the digits and add it to the number you started with. If your answer is a palindrome, you are finished. If not, you simply reverse the digits again and add. You keep repeating this step until a palindrome emerges. In base 10, numbers 1-9 are considered 0-step palindromes, as well as 11, 22, 33…99. They are not very interesting as you don’t have to do anything to them.

5. The other numbers take from 1 to 24 steps to produce a palindrome. Some 1step palindrome include 10, 21, 81, etc. the number 19 is an example of a 2-step palindrome. Step 1: 19 + 91 = 110 Step 2: 110 + 011 = 121 (a palindrome) Another example would by 89: a 3-step palindrome Step 1: 89 + 98 =

6. Some numbers take longer for a palindrome to appear. The number 89, for example, takes 24 steps, but most take much less than that. It has been found that almost any number will produce a palindrome using this method except for a very few. 196 is one such number. It has been carried out to millions of steps with no palindrome in sight. Another is 887. We can’t prove that these numbers will not produce palindromes but none have been found so far and it doesn’t look like any will be found.

7. Needless to say, mathematicians love to play with numbers like this. They create complex formulas to compute various palindromes and they spend day, weeks and even years finding bigger and bigger palindromes. They like to relate it to different types of numbers like prime numbers. One of the largest known palindromic prime, containing 30,913 digits was found by David Broadhurst in 2003.

8. As of January 2012, the largest proven palindrome generated by a formula was found containing 275,495 digits. So far, no use has been found for these unusual numbers, but who knows. After all, the original Mobius strip had no practical use when it was first discovered, but soon certain fan belts, 8-track tapes, etc. started using the idea and it prolonged the life of the belt, or tape. You don’t know what a Mobius strip is? Well, that is for another time…

9. Palindromes have popped up in some very strange places. Take this one, for instance, believed to be the oldest palindrome known, was found in Cirencester, England and it was also found in Pompeii, off the coast of Italy. It is believed to be associated with the early Christian movement.

10. Cited Sources Laycock, Mary, and Verda Holmberg. Aftermath II. Palo Alto: Dale Seymour, 1975. Print. "Making Numbers into Palindromes." The Math Forum. 1995. Web. 22 Apr. 2012.. Montfort, Nick, and William Gillespie. "A Palindrome Story." 2002: A Palindrome Story. Web. 22 Apr. 2012.. Schiller, Diane, and Mary Charles. "Moving Forward and Backward with Palindromes." Mathematics Teaching in the Middle School 10.2 (2004): 77-80. Print. "Solve This! Palindromes." Library.thinkquest.org/TQ0312134/palindromes.html. 2003. Web. 22 Apr. 2012..