Parabolas in Taxicab Geometry

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.…”