The hyperbolic conics in the hyperbolic geometry
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this work we have aimed to specify basic properties of hyper-bolic conics of uper half plane U and examined each conic at two steps: Firstly we have studied the case where center and focus(es) of the conic are on imaginary axis. Secondly we have transfered our findings to any conic by means of Mob(U). Although there are works on hyperbolic circles in sources such as[2], we also examine hyperbolic circles for readines. We have also seen that each conic family is invariant under the action of Mob(U).
Abstract
In this work we have aimed to specify basic properties of hyper-bolic conics of uper half plane U and examined each conic at two steps: Firstly we have studied the case where center and focus(es) of the conic are on imaginary axis. Secondly we have transfered our findings to any conic by means of Mob(U). Although there are works on hyperbolic circles in sources such as[2], we also examine hyperbolic circles for readines. We have also seen that each conic family is invariant under the action of Mob(U).
참고문헌 (7)
- J.W. Anderson, "Hyperbolic Geometry, Springer Undergraduate Mathematics Series" (1999), Springer-Verlag
- G.A. Jones, "Complex functions, an algebraic and geometric viewpoint" (1987), Cam-bridge University Press
- C.H. Edwards, Jr., "Calculus and Analytic Geometry" (1990), Prentice-Hall International, Inc.
- J.J. O’Connor, "Non-Euclidean Geometry", pp.1996, JOC
- "Non-Euclidean Geometry"[URL]
- "Seminar on the History of Hyperbolic Geometry"[URL]
- S. Hegedus, "MTH531 Geometry for Teachers-Week 7", ~ (2006)