Original scientific paper
A generalization of some well-known distances and related isometries
Harun Bariş Çolakoğlu
orcid.org/0000-0001-5559-9768
; Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences,Eskişehir Osmangazi University, Eskişehir, Türkiye
Rüstem Kaya
Abstract
In this paper, we define a family of distance functions in the
real plane, m-distance function, which includes the
taxicab, Chinese checker, maximum, and alpha distance functions as
special cases, and we show that the m-distance function
determines a metric. Then we give some properties of the
m-distance, and determine isometries of the plane with
respect to the m-distance. Finally, we extend the
m-distance function to three and n-dimensional spaces, and
show that each extended distance function determines a metric. We
also give some properties of the m -distance in three-dimensional space.
\end{abstract}
Keywords
metric; m-distance; taxicab distance; Chinese checker distance; maximum distance; alpha distance; minimum distance set; isometry
Hrčak ID:
68613
URI
Publication date:
10.6.2011.
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