The Road to Reality Study Notes: Difference between revisions
→2.5 Other representations of hyperbolic geometry
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* Conformal, so angles are preserved | * Conformal, so angles are preserved | ||
* Sends circles on the sphere to circles on the plane | * Sends circles on the sphere to circles on the plane | ||
It is then emphasized that each of these representations are merely ‘Euclidean models’ of hyperbolic geometry and are not to be taken as what the geometry actually ‘is’. In fact, there are more representations such as the [https://en.wikipedia.org/wiki/Minkowski_space Minkowskian geometry] of special relativity. The idea of a generalized ‘square’ is then presented in ''conformal'' and ''projective'' hyperbolic representations to show an interesting generalization of the Euclidean square. | It is then emphasized that each of these representations are merely ‘Euclidean models’ of hyperbolic geometry and are not to be taken as what the geometry actually ‘is’. In fact, there are more representations such as the [https://en.wikipedia.org/wiki/Minkowski_space Minkowskian geometry] of special relativity. The idea of a generalized ‘square’ is then presented in ''conformal'' and ''projective'' hyperbolic representations to show an interesting generalization of the Euclidean square. | ||