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...
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MDPI AG
2024-09-01
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| author | Antonella Nannicini Donato Pertici |
| author_facet | Antonella Nannicini Donato Pertici |
| author_sort | Antonella Nannicini |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0bb47d6a23f44d66a55e58e8df22af4e |
| institution | DOAJ |
| issn | 2673-9321 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Foundations |
| spelling | doaj-art-0bb47d6a23f44d66a55e58e8df22af4e2025-08-20T02:55:41ZengMDPI AGFoundations2673-93212024-09-014446848710.3390/foundations4040030On Geodesic Triangles in Non-Euclidean GeometryAntonella Nannicini0Donato Pertici1Department of Mathematics and Informatics “U. Dini”, University of Florence, Viale Morgagni, 67/a, 50134 Firenze, ItalyDepartment of Mathematics and Informatics “U. Dini”, University of Florence, Viale Morgagni, 67/a, 50134 Firenze, ItalyIn 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.https://www.mdpi.com/2673-9321/4/4/30non-Euclidean geometrynotable points of hyperbolic and spherical trianglespolar triangletotally geodesic hypersurfaces |
| spellingShingle | Antonella Nannicini Donato Pertici On Geodesic Triangles in Non-Euclidean Geometry Foundations non-Euclidean geometry notable points of hyperbolic and spherical triangles polar triangle totally geodesic hypersurfaces |
| title | On Geodesic Triangles in Non-Euclidean Geometry |
| title_full | On Geodesic Triangles in Non-Euclidean Geometry |
| title_fullStr | On Geodesic Triangles in Non-Euclidean Geometry |
| title_full_unstemmed | On Geodesic Triangles in Non-Euclidean Geometry |
| title_short | On Geodesic Triangles in Non-Euclidean Geometry |
| title_sort | on geodesic triangles in non euclidean geometry |
| topic | non-Euclidean geometry notable points of hyperbolic and spherical triangles polar triangle totally geodesic hypersurfaces |
| url | https://www.mdpi.com/2673-9321/4/4/30 |
| work_keys_str_mv | AT antonellanannicini ongeodesictrianglesinnoneuclideangeometry AT donatopertici ongeodesictrianglesinnoneuclideangeometry |