Binary Relations as Primitive Notions in Elementary Geometry

Abstract

Publisher Summary This chapter considers equidistance and the order of points on a line as the standard primitive notions of Euclidean, hyperbolic, or elliptic geometry. In specific, equidistance is a quaternary relation. The order of points on a line is described by the ternary relation of betweenness in Euclidean or hyperbolic geometry, and by the quaternary relation of cyclic order in elliptic geometry. the ternary relation of a point being equally distant from two other points can be used as the only primitive notion of Euclidean geometry of two or more dimensions. The chapter provides a detailed discussion of Pieri's relation. The chapter also describes binary relation as a suitable primitive notion for elliptic geometry.