On The Chinese Checkers Spherical Inversions in Three Dimensional Chinese Checkers Space

Abstract

In this paper, we study an inversion with respect to a Chinese checkers sphere in the three dimensional Chinese Checkers space, and prove several properties of this inversion. We also study cross ratio, harmonic conjugates and the inverse images of lines, planes and Chinese Checkers spheres in three dimensional Chinese Checkers space.

A Note on the Maximum Circle Inverses of Lines in the Maximum Plane

“…Moreover, inversion maps in an elipse, a sphere, an ellipsoid, parallel lines, central cones, star shape sets were defined and introduced, [8], [11], [18][19][20]. Besides, inversions with respect to a circle and a sphere in some non-Euclidean geometries such as the taxicab geometry, the Chinese Checkers geometry, the maximum geometry were defined and their basic properties were given, [5], [9], [10], [14][15][16][17], [22]. In this article, the images of lines under inversion in maximum circle have been analytically examined.…”