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Limits of Geometries in 2DAs we zoom in closer and closer, hyperbolic geometry beings to appear more and more euclidean (for instance, the angle sum of a very small triangle is very close to $\pi$). In fact, it is possible to embed a sequence of copies of hyperbolic geometry into projective geometry so that
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What is a Geometry? |
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What does it mean to take a Limit? |
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Statement of the problem. |
Important groups and their Lie algebras. |
Limits of Euclidean Geometry |
Limits of Hyperbolic Geometry |
Limits of Elliptic Geometry |