Browse > Article
http://dx.doi.org/10.11568/kjm.2014.22.3.567

A STUDY ON QUADRATIC CURVES AND GENERALIZED ECCENTRICITY IN POLAR TAXICAB GEOMETRY  

Kim, Kyung Rok (GyeongGi Science High School)
Park, Hyun Gyu (GyeongGi Science High School)
Ko, Il Seog (GyeongGi Science High School)
Kim, Byung Hak (Department of Applied Mathematics and Institute of Natural Sciences Kyung Hee University)
Publication Information
Korean Journal of Mathematics / v.22, no.3, 2014 , pp. 567-581 More about this Journal
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.
Keywords
polar taxicab distance; eccentricity;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Kyung Rok Kim, Hyun Gyu Park, Il Seog Ko, and Byung Hak Kim, On Polar Taxicab Geometry in a Plane, to appear in Journal of Applied Mathematics and Informatics.
2 E. F. Krause, Taxicab Geometry, Addison-Wesley Publishing Company, Menlo Park, 1975
3 Chae Hee Oh, Il Seog Ko, and Byung Hak Kim, Area of Triangle in the Plane With ${\alpha}$-Distance Function, Journal of the Korean Society of Mathematical Education 19 (4) (2012), 337-347.   과학기술학회마을   DOI   ScienceOn
4 Gokhan Soydan, Yusuf Dogru, and N. Umut Arslandogan, On the Ratio of Directed Lengths on the Plane with Generalized Absolute Value Metric and Related Properties, Filomat 2012 26 (1) (2012), 119-129.
5 S. Tian, ${\alpha}$-Distance - A generalization of Chinese Checker Distance and Taxicab Distance, Misouri Journal of Mathematical Sciences 17 (1) (2005), 35-40.
6 Dong-Soo Kim, Soojeong Seo, Woo-in Beom, Deukju Yang, Juyeon Kang, Jieun Jeong, and Booseon Song, Some Equivalent Conditions for Conic Sections, Journal of the Korean Society of Mathematical Education 19 (4) (2012), 315-325.   과학기술학회마을   DOI   ScienceOn
7 A. Bayar, S. Ekmekci, and Z. Akca, On the Plane Geometry with Generalized Absolute-Value Metric, Mathematical Problems in Engineering 2008 (2008), 1-8.
8 R. Kaya, O. Gelisken, S. Ekmekci, and A. Bayar, Isometries of the Plane with Generalized Absolute Value Metric, submitted to Rocky Mountains.
9 Rusem Kaya and Harun Baris Colakoglu, Taxicab Versions of Some Euclidean Theorems, IJPAM 26 (1) (2005), 69-81.