Monday, January 24, 2011

Geomagic Squares

Lee Sallows has written his own brief, self-deprecating bio on the Web as follows:
"Born in 1944 and raised in post-war London, Lee Sallows has lived in Nijmegen in The Netherlands for the past 40 years. Until recently he worked as an electronics engineer for the Radboud University. A handful of published articles on computational wordplay and recreational mathematics are the only fruits of an idle, if occasionally inventive, life."
I'm familiar with Lee from his fascinating, creative work with "self-enumerating" sentences and pangrams covered in some of Douglas Hofstadter's books (but also available online). Here's one sentence he invented that became famous in certain circles:
"Only the fool would take trouble to verify that his sentence was composed of ten a's, three b's, four c's, four d's, forty-six e's, sixteen f's, four g's, thirteen h's, fifteen i's, two k's, nine l's, four m's, twenty-five n's, twenty-four o's, five p's, sixteen r's, forty-one s's, thirty-seven t's, ten u's, eight v's, eight w's, four x's, eleven y's, twenty-seven commas, twenty-three apostrophes, seven hyphens and, last but not least, a single !"
Recently, Alex Bellos posted about Lee's latest creative venture into "geomagic squares":

For some reason that post didn't initially grab me much, 'til I noticed the concept getting more and more play around the Web. Peter Cameron's post drove home for me that once again Sallows is on to something deeper than first meets the eye:

Sallows' own intro to the subject is here:

Geomagic squares have to do, in a sense, with patterns... of patterns; and 'magic number squares' (with which most of you are familiar) are simply a special case of Sallows' new broader category. I think Martin Gardner would've gotten quite a kick out of this new li'l creation, and hopefully many of you will as well!

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