Editing The Road to Reality Study Notes
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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 âEuclidean modelsâ of hyperbolic geometry and are not to be taken as what the geometry actually âisâ. 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 âsquareâ 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 âEuclidean modelsâ of hyperbolic geometry and are not to be taken as what the geometry actually âisâ. 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 âsquareâ is then presented in ''conformal'' and ''projective'' hyperbolic representations to show an interesting generalization of the Euclidean square. |