On Geodesic Triangles in Non-Euclidean Geometry
In this paper, we study centroids, orthocenters, circumcenters, and incenters of geodesic triangles in non-Euclidean geometry, and we discuss the existence of the Euler line in this context. Moreover, we give simple proofs of the existence of a totally geodesic 2-dimensional submanifold containing a given geodesic triangle in the hyperbolic or spherical 3-dimensional geometry.
Authors
- Donato Pertici (ORCID: https://orcid.org/0000-0003-4667-9568)
- Antonella Nannicini (ORCID: https://orcid.org/0000-0001-5149-706X)
Institutions
- University of Florence (IT)
Publication Details
- Journal
- Foundations
- Published
- 2024-09-26
- DOI
- https://doi.org/10.3390/foundations4040030
- Primary Topic
- Mathematics and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00