The palindrome, especially palindromic dates, have gained attention with the recent occurrence of 11/02/2011 and 11/11/11. So now is an opportune time to explore variations on the theme.
If you have a series of letters or numbers and you stand on your head, what does it look like? Can it be a palindrome? Is it the same as an ordinary palindrome?
Before everybody hyperventilates about having to do yoga-like contortions just to find out some esoteric fact about words or dates, let me point out that if you rotate the page, you get the same effect as standing on your head. Whew. That simplifies things. So let's get to the meaty stuff.
Rotational Palindromes
I've given a name to this special kind of sequence of words or numbers. A rotational palindrome is such a sequence that reads the same when you turn the paper it's written on upside down, i.e., rotated it 180 degrees. A little thought makes it obvious that any palindrome containing only the letters (using caps) H, I, O, S, X, and Z will work. These words are ordinary palindromes, and are not very interesting: SIS and S.O.S. are the only ones that come easily to mind.
There is one additional pair of letters that, if placed symmetrically about the center, will make a more interesting rotational palindrome: M and W (all right, depending on how you form the letters, you might need a little literary license). Then the word MOW is a rotational palindrome, but not an ordinary one.
Rotational Number Palindromes
Any palindromic number containing only 0, 1, and 8 is also a rotational palindrome (again we need a little leeway with the one). But, again, there is one pair of numbers that can form a rotational palindrome but not an ordinary one: 6 and 9.
Ordinary Rotational Palindromic Dates
Ordinary palindromic dates that are also rotational palindromes are rare---most of them are in the past. The last one was 08/11/1180. They retired ordinary rotational palindromic dates for a long time after that. The next one will be 10/08/8001.
Pure Rotational Palindromes
A "pure" rotational palindrome is one that is not an ordinary palindrome. One such number palindrome is 69, just to take a random example. As far as dates go, there are some closer to home than the ordinary rotational palindromic dates.
06/11/1190 was the last pure rotational palindromic date, less than ten years after the last regular palindromic date. Can you imagine living in such an exciting time? The next one? That'll be 10/09/6001, almost exactly 2 millennia before the next normal rotational palindromic date. That's October ninth in America. Europeans, always ahead of us Yanks it seems, can celebrate 29 days earlier on Sept. 10.
A Date With Historical Implications
There is one pure rotational palindromic date that may still have significance, though it is so far in the future that there's no guarantee anyone will be around to take notice. That date, written in the continental style, is 11/09/6011.
Jon Plotkin - The author was a math major at Cornell and has a master's degree in meteorology from MIT.
