Group of Isometries of the CC-Plane

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

“…Proof. Since the translation preserve distances in the Chinese Checkers space [15], [12] by translating in R 3 C (0; 0; 0) to (a; b; c) one can easily get the value of x 0 ; y 0 and z 0 .…”

The Isometry Group of Chinese Checker Space

“…Three dimensional CC-space has been introduced and studied analytically by Gelisgen-Kaya-Ozcan [6]. In this work which is motivated by [9] and [8], we extend the result of CC-plane to three dimensional CC-space and determine the group of isometries of it.…”

On the ratio of directed lengths on the plane with generalized absolute value metric and related properties

“…Since the plane with the generalized absolute value metric has distance function different from that in the Euclidean plane, it is interesting to study on the plane with the generalized absolute value metric of topics that include the distance concept in the Euclidean plane. ( [1], [2], [4], [5], [6], [7], [9], [12], [10], [11], [13], [14], [16], [23], [24], [25], [19], [26], [27], [28], [29]) These topics are division point, directed lengths, ratio of directed lengths, Menelaus'es Theorem, Ceva's Theorem and the theorem of directed lines. In this paper, GAM is the abbreviation for the plane geometry with the generalized absolute value metric.…”