Taxicab Geometry

Abstract

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.

A conjecture both deep and profound Is whether a circle is round. In a paper by Erdös, Written in Kurdish, A counterexample is found.

—Anonymous