A finite geometry of twenty-five points

AbstractThis thesis has taken an axiomatic system for a finite geometry with a five-point line, introduced definitions of various familiar figures and relationships, and determined properties of the figures in this system. Many of the theorems found herein are true in ordinary Euclidean geometry, but several interesting properties also arise in contrast to the usual.Given consideration in this development are properties of parallelism, perpendicularity, and congruence, in a study of lines, segments, triangles, and quadrilaterals. Also included in the presentation is an introduction to circles and parabolas.Ball State UniversityMuncie, IN 47306