Turkish Journal of Mathematics
Abstract
In this paper, we give a generalization of the well-known Minkowski distance family in the $n$-dimensional Cartesian coordinate space. Then we consider three special cases of this family, which are also generalizations of the taxicab, Euclidean, and maximum metrics, respectively, and we determine some circle properties of them in the real plane. While we determine some properties of circles of these generalized distances, we discover a new definition of ellipses, and then we also determine a similar definition of hyperbolas, which will be new members among different metrical definitions of central conics in the Euclidean plane.
DOI
10.3906/mat-1904-56
Keywords
Minkowski distance, $l_{p}$-norm, $l_{p}$-metric, taxicab distance, Manhattan distance, Euclidean distance, maximum distance, Chebyshev distance, ellipse, hyperbola, central conics, asymptote, eccentrix, eccentricity
First Page
319
Last Page
333
Recommended Citation
ÇOLAKOĞLU, HARUN BARIŞ
(2020)
"A generalization of the Minkowski distance and new definitions of the central conics,"
Turkish Journal of Mathematics: Vol. 44:
No.
1, Article 22.
https://doi.org/10.3906/mat-1904-56
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss1/22
