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Reflections on hyperbolic space
Snapshots of modern mathematics from Oberwolfach
Reflections on hyperbolic space
In school, we learn that the interior angles of any triangle sum up to π. However, there exist spaces different from the usual Euclidean space in which this is not true. One of these spaces is the “hyperbolic space”, which has another geometry than the classical Euclidean geometry. In this snapshot, we consider the geometry of hyperbolic polytopes, for example polygons, how they tile hyperbolic space, and how reflections along the faces of polytopes give rise to important mathematical structures. The classification of these structures is an open area of research.
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DOI (Digital Object Identifier)
10.14760/SNAP-2021-007-EN
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Reflections on Mathematics