A ltering one or more postulates of Euclidean geometry makes it possible to construct all kinds of strange geometries that are just as consistent, or free of internal contradictions, as the plane geometry taught in secondary schools. Some of these non-Euclidean geometries have turned out to be enormously useful in modern physics and cosmology, but the two most important, elliptic geometry and hyperbolic geometry, have a structure that is impossible to visualize. Hence most laymen find these geometries too difficult to comprehend and are certainly not able to search their structure for new theorems or to work on interesting non-Euclidean problems.
KeywordsEuclidean Geometry Constant Difference Opposite Comer Degenerate Ellipse Mobius Band
Unable to display preview. Download preview PDF.
- Square Circles. Francis Sheid in The Mathematics Teacher ,Vol. 54, No. 5, pages 307–312; May 1961.Google Scholar
- Square Circles. Michael Brandley, in The Pentagon ,pages 8–15; Fall 1970.Google Scholar
- Taxicab Geometry—A Non-Euclidean Geometry of Lattice Points. Donald R. Byrkit in The Mathematics Teacher ,Vol. 64, No. 5, pages 418–422; May 1971.Google Scholar
- Taxicab Geometry. Eugene F. Krause. Addison-Wesley Publishing Company, 1975. Dover reprint 1986.Google Scholar
- Taxicab Trigonometry. Ruth Brisbin and Paul Artola in Pi Mu Epsilon Journal ,Vol. 8, pages 89–95; Spring 1985.Google Scholar
- A Fourth Dimensional Look into Taxicab Geometry. Lori J. Mertens in Journal of Undergraduate Mathematics ,Vol. 19, pages 29–33; March 1987.Google Scholar