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Reflections on hyperbolic space

Instantanés de recherche mathématique à 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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Sujet mathématique

Algèbre et théorie des nombres
Géométrie et Topologie

Liens avec d'autres domaines

Sciences de la vie

Auteur(s)

Anna Haensch

Licence

DOI

10.14760/SNAP-2021-007-EN

Télécharger PDF

snapshot-2021-007.pdf

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      Sujet mathématique

      Algèbre et théorie des nombres
      Analyse
      Pédagogie et éducation
      Mathématiques discrètes et fondements des mathématiques
      Géométrie et Topologie
      Calcul numérique et calcul scientifique
      Théorie des probabilités et statistique

      Liens avec d'autres domaines

      Chimie et sciences de la terre
      Informatique
      Ingénierie et technologie
      Finances
      Humanités et sciences sociales
      Sciences de la vie
      Physique
      Pensées mathématiques

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