Bill Yates

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+Vladimir Bulatov does it again! At each moment, this movie shows you a tiling of the hyperbolic plane by pentagons, four meeting at each corner, mapped onto a disc with four slits cut out. This mapping is

For a more detailed explanation, with tons of great pictures, go here: http://bulatov.org/math/1001/

Here's the short version: there's a way to measure distances on a disk that makes it into a model of the hyperbolic plane. There are actually a number of ways, but Bulatov - and Escher - use the

For more details, try these picture-packed pages:

http://en.wikipedia.org/wiki/Conformal_map

http://en.wikipedia.org/wiki/Poincar%C3%A9_disk_model

and this more advanced one:

http://en.wikipedia.org/wiki/Riemann_mapping_theorem

#sciencesunday

**conformal**, meaning that it preserves angles. As time passes, the hyperbolic plane rotates and we see this crazy movie.For a more detailed explanation, with tons of great pictures, go here: http://bulatov.org/math/1001/

Here's the short version: there's a way to measure distances on a disk that makes it into a model of the hyperbolic plane. There are actually a number of ways, but Bulatov - and Escher - use the

**Poincare disk model**, because in this model straight lines look like portions of circles: very pretty. Then, according to the**Riemann mapping theorem**you can map this disk in a conformal way onto a disk with 4 slits cut out. The hard part is finding a formula for how to do it, and then implementing it on a computer.For more details, try these picture-packed pages:

http://en.wikipedia.org/wiki/Conformal_map

http://en.wikipedia.org/wiki/Poincar%C3%A9_disk_model

and this more advanced one:

http://en.wikipedia.org/wiki/Riemann_mapping_theorem

#sciencesunday

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I haven't read the Illuminatus trilogy, but the Atlas Sucked summary is pretty good.

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Too funny.

(via Little White Lion on Facebook)

(via Little White Lion on Facebook)

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They could have picked any name, but I never understood why it was the Tea Party. I'm not one for erasing history, but when kids learn about the Tea Party in school, I'd rather it be the Boston one. The rest is just embarrassing.

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