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Topic started by DualSpace on 29 Dec 2010, 19:48:35
DualSpace
Elite Member
Canada
Posts: 517
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29 Dec 2010, 19:48:35
 
Inspiration - hyperbolic geometry
Here's a fun image from Escher demonstating hyperbolic geometry on the poincare disk. Follow the triangles to see the angles for any triangle are less than 180 degrees. Poincare showed that 'most' manifolds are hyperbolic using this disk - but you need to remember some fundamental ideas about manifolds and charts, that you can connect a point exiting one part of the disk and connect it to the entry point of another part of the disk. These 'exit' and 'entries' are related to 2-D tori (multi-holed donuts, that any well-behaved 2-D manifold can be reduce to...). A sheet of paper can be rolled so the exit and entries attach, like a donut. Poincare used that, and his disk, to generate an infinite number of hyperbolic manifolds. Happy holidays......I live in hyperspace :P
 

Edited on 29 Dec 2010 at 19:49:32
TrencherKnight
Founding Member
United States
Posts: 396
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1 Jan 2011, 20:12:10
In reply to DualSpace
Re: Inspiration - hyperbolic geometry
For some reason this reminds me of Spy vs Spy
Spud
Elite Member
Australia
Posts: 1803
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1 Jan 2011, 21:26:04
In reply to TrencherKnight
Re: Inspiration - hyperbolic geometry

 

Edited on 1 Jan 2011 at 21:26:32