On Reduced Triangles in Normed Planes

Alonso, Jesús José Beltrán de Heredia; Martini, Horst; Spirova, Margarita

doi:10.1007/s00025-013-0313-y

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Cited by 3 publications

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“…For more results concerning reduced triangles in Minkowski planes, especially their metric properties, see also [5]. We deduce the following statements from Averkov's Theorems, basically starting with the dual and making use of the term AG-quasiregularity.…”

Section: T Is Equilateral Inmentioning

confidence: 70%

Geometry of Simplices in Minkowski Spaces

Leopold

Martini

2018

Results Math

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There are many problems and configurations in Euclidean geometry that were never extended to the framework of (normed or) finite dimensional real Banach spaces, although their original versions are inspiring for this type of generalization, and the analogous definitions for normed spaces represent a promising topic. An example is the geometry of simplices in non-Euclidean normed spaces. We present new generalizations of well known properties of Euclidean simplices. These results refer to analogues of circumcenters, Euler lines, and Feuerbach spheres of simplices in normed spaces. Using duality, we also get natural theorems on angular bisectors as well as inand exspheres of (dual) simplices.

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Section: T Is Equilateral Inmentioning

confidence: 70%