Geometric properties of polygons in Minkowski planes

• Loidybeth Carrillo Colmenares Departamento de Matemática, Facultad Experimental de Ciencias, Universidad del Zulia
• Tobías Rosas Soto Departamento de Matemática, Facultad Experimental de Ciencias, Universidad del Zulia

Keywords: Minkowski planes, polygons, centroid, C-orthocenter, antipolygons

Abstract

In this article we study the geometric properties of two type of polygons in the normed and affine plane R², such as: quadrilaterals and pentagons. The notion of antiquadrilateral is generalized for any quadrilateral, with respect to a point in the plane and we introduce the notion of C-orthocenter to inscribed quadrilaterals on a circumference. On the same way we define the notoion antipentagon for any pentagon in the normed and affine plane R², with respect to a given point and so we introduce the notion of C-orthocenter to inscribed pentagons on a circumference. The geometric relations of the barycentre of this polygons, its antipolygons, the triangles formed by its vertices and some points related to these triangles,
such as: baricenters, circumcenters and C-orthocenters (when they exist), are determined. The Geogebra program was used for the modeling of figures in the euclidean plane R².

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