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Roelof de Groot
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Lives in Amsterdam
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Roelof de Groot

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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 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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Edwin Slothouber's profile photo
 
Wow, nice!
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Roelof de Groot

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Pick it up!
Mohit Muthanna originally shared:
 
LOL! This is hilarious, sad, awesome, and hilarious again, all in one sheet.
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I like.
Steven Wittens originally shared:
 
I redesigned my website and pulled out all the stops.
A blog about random hacks, graphics and design, math and other ephemera.
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Bij wet verplichten is wel overdreven. Misschien moet je gewoon opstappen als je geen kraanwater krijgt.
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Een eenvoudige site voor een pilotproject voor gespreksbegeleiding in de zorg. In samenwerking met Mevrouw Vanmulken.
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"Eye ball". The red circle appears to move when observers slowly swing their faces. For those who wear concave glasses, the red circle appears to move in the same direction as the swing or t...
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