Devoted to a domain of plane geometry, defining not only concepts of incidence but also metric concepts such as orthogonality or reflection. Verifies the interrelationships of three theories showing how they are different representations of a single, unified theory. These include a purely geometric theory based on the concept of incidence structures with orthogonality or with reflections, mainly as a treatment of Euclidean and non-Euclidean planes and certain subplanes of these planes; a theory of three-dimensional metric vector spaces with their natural geometric interpretation; and a theory of special types of S-groups and their group planes.

Metric Planes and Metric Vector Spaces

Science & Math

Lingenberg, R.

Mathematics

wiley

<p>In recent decades research into the foundations of geometry has completely transformed the field and created a need for new methods of presenting geometry at the university level. Rudiments of Plane Affine Geometry develops rigorously and clearly one geometric theory accessible to the reader with no previous experience. It reflects the spirit and displays some of the basic ideas of modern geometric axiomatics. The volume is intended for undergraduates with a modest knowledge of algebra and linear algebra and provides a sound introduction to deductive geometry.</p>  <p>(Mathematical Expositions No. 20)</p>

Rudiments of Plane Affine Geometry: Mathematical Expositions No. 20 (Heritage)

Scherk, P.

History & Philosophy

University of Toronto Press, Scholarly Publishing

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