A study on quadratic curves and generalized eccentricity in polar taxicab geometry
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초록
Over the years, there has been much research conducted on quadratic curves and the set of points with the generalized notion of eccentricity in a plane with metrics such as taxicab distance or Chinese-checker distance. On the other hand, polar taxicab distance has been newly proposed on the polar coordinate system, a type of curvilinear coordinate system, to overcome the limitation of pre-existing metrics in terms of describing curved routes. Previous study has looked into the fundamental properties of this metric. From this point of view, we study the quadratic curves and the set of points with the generalized notion of eccentricity in a plane with polar taxicab distance.
Abstract
Over the years, there has been much research conducted on quadratic curves and the set of points with the generalized notion of eccentricity in a plane with metrics such as taxicab distance or Chinese-checker distance. On the other hand, polar taxicab distance has been newly proposed on the polar coordinate system, a type of curvilinear coordinate system, to overcome the limitation of pre-existing metrics in terms of describing curved routes. Previous study has looked into the fundamental properties of this metric. From this point of view, we study the quadratic curves and the set of points with the generalized notion of eccentricity in a plane with polar taxicab distance.
참고문헌 (9)
- A. Bayar, "On the Plane Geometry with Generalized Absolute-Value Metric", Mathematical Problems in Engineering, 2008, pp.1~8 (2008)
- R. Kaya, "Isometries of the Plane with Generalized Absolute Value Metric", Rocky Mountains
- Rusem Kaya, "Taxicab Versions of Some Euclidean Theorems", IJPAM, 26(1), pp.69~81 (2005)
- 김동수, "SOME EQUIVALENT CONDITIONS FOR CONIC SECTIONS", 순수 및 응용수학, 19(4), pp.315~325 (2012), 한국수학교육학회
- Hyun Gyu Park, "ON POLAR TAXICAB GEOMETRY IN A PLANE", Journal of Applied Mathematics and Informatics, 32(5), pp.783~790 (2014), 한국전산응용수학회
- E. F. Krause, "Taxicab Geometry" (1975), Addison-Wesley Publishing Company
- 오채희, "AREA OF TRIANGLE IN THE PLANE WITH ALPHA DISTANCE FUNCTION", 순수 및 응용수학, 19(4), pp.337~347 (2012), 한국수학교육학회
- Gokhan Soydan, "On the Ratio of Directed Lengths on the Plane with Generalized Absolute Value Metric and Related Properties", Filomat, 26(1), pp.119~129 (2012)
- S. Tian, "α-Distance - A generalization of Chinese Checker Distance and Taxicab Distance", Misouri Journal of Mathematical Sciences, 17(1), pp.35~40 (2005)
