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.
Highlights
In the game of Chinese checkers, checkers are allowed to move in the vertical, horizontal, and diagonal directions
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 study cross ratio, harmonic conjugates and the inverse images of lines, planes and Chinese Checkers spheres in three dimensional Chinese Checkers space
Summary
In the game of Chinese checkers, checkers are allowed to move in the vertical (north and south), horizontal (east and west), and diagonal (northeast, northwest, southeast and southwest) directions. In [7], Krause asked how to develop a distance function that measures and made a suggestion for the idea of Chinese Checkers geometry and in G. Chen, introduced it by de...ning the metric in the coordinate plane [22]. The circle inversion have been generalized in three-dimensional space by using a sphere as the circle of inversion [16]. We de...ne an inversion with respect to a Chinese Checkers sphere and prove several properties of this new transformation. We introduce inverse points, cross ratio, harmonic conjugates and the inverse images of lines, planes and Chinese Checkers spheres in three dimensional Chinese Checkers space
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