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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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Mathematical subjects
Algebra and Number Theory
Geometry and Topology
Connections to other fields
Life Science
License
DOI (Digital Object Identifier)
10.14760/SNAP-2021-007-EN
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Mathematical subjects
Algebra and Number Theory
Analysis
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics
Connections to other fields
Chemistry and Earth Science
Computer Science
Engineering and Technology
Finance
Humanities and Social Sciences
Life Science
Physics
Reflections on Mathematics