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Project Euler has this problem called Laserbeam. It starts as one thing but leads somewhere completely different.

Mais uma para a série: "derivadas alternativas"

bad maths that gives the right answer 

Uma cidade perfeita para os exercícios de matemática!

Satellite map of Missoula, Montana

More on the Spectre

Images from this great Yoshiaki Araki thread. (If you're interested in tessellations and are twitterpated, he's a must follow.)

He links the Nature article (good and a free read).

Best one, so far:

Robert Farthauer suggests:

And, of course, the actual article, by David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss.

Kaplan gives this illustration of the tile:

He has a one page stop for info about the tiling.

Bonus: via New-Cleckit Dominie

INTERNATIONAL KWEEN OF TRIGONOMETRY

Created by Dave Richeson.

Bridget Riley Arrest Riffs

Started playing with this before realizing it is yet another Bridget Riley pattern. She gets me. Play in GeoGebra.

It’s a serious issue!

Did you know that there is a way of cutting an equilateral triangle into seven similar triangles that have pairwise different sizes, and they are not right triangles? (With right triangles it is easy to cut into any number of similar pieces.)

One of the angles in each triangle is 120 degrees and the other two are roughly 40.67915375798 and 19.32084624 degrees. You can read the details in the paper:

A note on perfect dissections of an equilateral triangle by Andrzej Zak