Squaring the square

December 4, 2007 4:41 AM

Nowhere-neat tilings are actually pretty neat. We all know you can't "square the circle", but do you know the story of squaring the square? (And by the way, even if you can't construct π with a ruler and compass, you can come awfully close without too much work.)
posted by Wolfdog (10 comments total)

From what rudimentary understanding I can gain of all this at this time in the morning, it's looking to be pretty neat indeed. If I wanted to decorate a wall like this, would I need to hire a mathematician as my interior decorator?



My understanding will be no less rudimentary at 2 in the afternoon.
posted by PhatLobley at 5:04 AM on December 4, 2007

Most of those look like variations of a pinwheel pattern.
(This is neat. Thanks for the post!)
posted by Balisong at 6:26 AM on December 4, 2007

It's interesting that all of the tilings of squares except 39x39 (at least on the first page - the second wouldn't load for me) have either rotational or reflectional symmetry. Are the "pretty" ones just easier to find?
posted by Horselover Fat at 8:06 AM on December 4, 2007

I like how they look twisted because of the color contrasts.
posted by weapons-grade pandemonium at 8:11 AM on December 4, 2007

Awesome. The Tutte link is fantastic stuff.

*pours one out for Paul Erdos*

If I wanted to decorate a wall like this, would I need to hire a mathematician as my interior decorator?

You'd probably do well enough with some graph paper and some spare time, if you were mostly concerned with the general look rather than the precise nowhere-neat constraints.
posted by cortex at 8:50 AM on December 4, 2007

Grout forgives a lot of mathematical sins.
posted by ardgedee at 10:09 AM on December 4, 2007 [1 favorite]

That first link is off the homepage of Joseph DeVincentis, who is a sort of a hero of mine when it comes to recreational mathematics.
posted by vacapinta at 10:31 AM on December 4, 2007

Sometimes I think I'm okay at math and then I look at something like this and realize I am practically a moron.
posted by autodidact at 12:40 PM on December 4, 2007

Man, that Ramanujan was something special. (Also read about the number 1729.)
posted by phliar at 3:22 PM on December 4, 2007

this is really cool
posted by es_de_bah at 5:06 PM on December 4, 2007