Monday, 9 June 2014

Pig Latin Magic Square

My friend David Brooks just sent me this breaking Math News from Old Hickory, Tn on a newly discovered (June 8, 2014) Alpha-Magic Square :

consider  the following magic square:

Now this is the Pig-Latin (or if you prefer, Igpay Atinlay, notation of these same numbers:

Now count the number of letters in each word and replace them with the counts:
And in the words of Brahma Gupta..... BEHOLD!

My thanks to David Brooks the input

I recently learned that the idea of alphamagic squares is very young.  They were first invented by English Engineer and recreational mathematician Lee Sallows in 1986 Sallows, L. C. F. "Alphamagic squares." Abacus 4 (No. 1): 28-45, 1986.) Sallows is also known for inventing golygons, a polygon containing only right angles, such that adjacent sides exhibit consecutive integer lengths. He also recently discovered a very clever relationship about the triangles formed by the medians of another triangle, for which I was able to add a small extension.

It turns out that there is a surprisingly large number of alphamagic squares, not only in English but also in many other languages. In French, there is just one alphamagic square involving numbers up to 200, but an additional 255 squares if the size of the entries is increased to 300. For entries less than 100, none occurs in Danish or in Latin, but 6 occur in Dutch, 13 in Finnish, and an incredible 221 in German.
(From David
I have not seen a alphamagic square larger than 3x3, but they seem to be possible.....Anyone, Anyone, ......Bueller?
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