While we determine some properties of circles of these generalized distances, we discover a new definition ofellipses, and then we also determine a similar definition of hyperbolas, which will be new members among differentmetrical definitions of central conics in the Euclidean plane.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we give a generalization of the well-known Minkowski distance family in the n-dimensionalCartesian coordinate space.
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Key Findings & Data:Then we consider three special cases of this family, which are also generalizations of thetaxicab, Euclidean, and maximum metrics, respectively, and we determine some circle properties of them in the realplane.
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Conclusion & Impact:While we determine some properties of circles of these generalized distances, we discover a new definition ofellipses, and then we also determine a similar definition of hyperbolas, which will be new members among differentmetrical definitions of central conics in the Euclidean plane.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, we give a generalization of the well-known Minkowski distance family in the n-dimensionalCartesian coordinate space. Then we consider three special cases of this family, which are also generalizations of thetaxicab, Euclidean, and maximum metrics, respectively, and we determine some circle properties of them in the realplane. While we determine some properties of circles of these generalized distances, we discover a new definition ofellipses, and then we also determine a similar definition of hyperbolas, which will be new members among differentmetrical definitions of central conics in the Euclidean plane.
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Cite This Article
ÇOLAKOĞLU, H. B. (2022). A generalization of the Minkowski distance and new definitions of the central conics. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 1, 319–333. https://ajindex.com/articles/608786
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