On the distance formulae in the generalized taxicab geometry

Authors: HARUN BARIŞ ÇOLAKOĞLU

Abstract: In this paper, we first determine the generalized taxicab distance formulae between a point and a line and two parallel lines in the real plane, then we determine the generalized taxicab distance formulae between a point and a plane, two parallel planes, a point and a line, two parallel lines and two skew lines in three dimensional space, giving also the relations between these formulae and their well-known Euclidean analogs. Finally, we give the generalized taxicab distance formulae between a point and a plane, a point and a line and two skew lines in $n$-dimensional space, by generalizing the concepts used for three dimensional space to $n$-dimensional space.

Keywords: Generalized taxicab distance, metric, generalized taxicab geometry, three dimensional space, $n$-dimensional space

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