Colossal Gardner, ch. 3


The last chapter of the arithmetic and algebra section is on palindromes. I absolutely love the “near miss” palindrome at the front of the article, attributed to Ethel Merperson, in Son of the Giant Sea Tortoise, edited by Mary Ann Madden (Viking, 1975) –

A man, a plan, a canal – Suez!

Palindromes can take many forms, from words and sentences that can be read the same forward and backward, numbers that can be rotated, palindromic primes, and even photos of things (like a bird in flight, going from wing tip to wing tip).

Here’s a game. Start with any positive integer. Reverse it and add the two numbers together. There’s a conjecture that you’ll get a palindrome after a finite number of steps.

47
74

121  <— End

183
381

564
465

1029
9201
—-
10230
3201
—-
13431 <- End

There have been papers written on the existence of palindromic primes and powers. You can play with palindromic roots to get palindromic squares, such as 121^2 = 14641.

You can find many of the same language examples in the wiki article. Yreka City in California used to have the Yreka Bakery and Yrella Gallery. Then there was the former premier of Cambodia, Lon Nol. And, you can have sentences where the word order is palindromic: from J. A. Lindon – “You can cage a swallow, can’t you, but you can’t swallow a cage, can you?”

Note: Lindon was a pioneer in the recreational mathematics field of anti-magic squares. In magic squares, the rows and columns all add up to the same number. With anti-magic squares, the sums of the rows, columns and diagonals are all different. He died in 1979.

Challenge: Can you find a copy of J. A. Lindon’s “Doppelganger,” and can you write a longer palindromic poem yourself?

Comments: I love palindromes, and I had a book collection of them at one time. Back when I first had a 4-banger calculator, I’d tried to find palindromic numbers. I’ve never heard of anti-magic squares before, but they could be fun to play with.

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