A Simple Non-Euclidean Geometry and Its Physical Basis

There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' colleges-a reflec­ tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers.