Geometry of simplices in Minkowski spaces
نویسندگان
چکیده
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.
منابع مشابه
On the Geometry of Simplices in Minkowski Spaces
Let T be a d-dimensional simplex in a d-dimensional real normed space (= Minkowski space). We introduce a special Minkowskian area-measure and Minkowskian trilinear coordinates with respect to T, allowing us to study Minkowskian balls which are tangent to all hyperplanes determined by the facets of T. Finally we apply the derived statements to characterize simplices having special Minkowskian p...
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