Euclidean Rotation in Taxicab Geometry
- Author:
- Dr. Jack L. Jackson II
Euclidean Rotation in Taxicab Geometry
In Euclidean Geometry a rotation about a point preserves both distance and angle measures. Therefore, a preimage is mapped to a congruent image.
However, in Taxicab Geometry this is not true. Since angles are measured the same in Taxicab and Euclidean Geometries, a rotation still preserves angle measures in Taxicab Geometry. However, a rotation does not preserve distances, since the distance depends on the angle with the x-axis. A Euclidean rotation does not map a preimage to a congruent image in Taxicab Geometry.