A generalization of the Minkowski distance and new definitions of the central conics

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ÇOLAKOĞLU H. B.

TURKISH JOURNAL OF MATHEMATICS, vol.44, no.1, pp.319-333, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-1904-56
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.319-333
  • 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
  • Akdeniz University Affiliated: Yes

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.