Symmetric distance formula in kantor spaces and the radius of the circumscribed sphere of affinely independent set of points

Abstract

Mass points are very useful objects not only in physics but also in geometry. There are several ways to approach the mathematics of mass points. In this paper we give an independent interpretation. We define kantor space and kantors as the elements of it. We prove that this is a vector space and give a short overview of the types of bases and the connections between them. One of our important tools is the symmetric distance formula for kantors, which expresses the distance of two points in terms of their kantric coordinates. We introduce the kantric scalar product, which allows us to prove easily the existence of an orthogonal point and give a formula of the radius of the circumscribed sphere of affinely independent set of points, which is our main result.