文章基本信息

标题：Osculating Circles of Conics in Cayley-Klein Planes
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作者：Weiss, Gunter ; Sliepčević, Ana
期刊名称：KoG
印刷版ISSN：1331-1611
电子版ISSN：1846-4068
出版年度：2010
卷号：13
期号：13
页码：7-12
出版社：Croatian Society for Geometry and Graphics
摘要：In the Euclidean plane there are several well-known methods of constructing an osculating (Euclidean) circle to a conic. We show that at least one of these methods can be “translated” into a construction scheme of finding the osculating non-Euclidean circle to a given conic in a hyperbolic or elliptic plane. As an example we will deal with the Klein-model of these non-Euclidean planes, as the projective geometric point of view is common to the Euclidean as well as to the non-Euclidean cases.
关键词：Cayley-Klein plane; elation; pencil of conics; osculating circle; curvature centre