Two new sets of ellipse-related concyclic points

被引：5

作者：

Ternullo, Maurizio ^{[1
]}

机构：

[1] Citta Univ Catania, Osservatorio Astrofis Catania, INAF, I-95123 Catania, Italy

来源：

JOURNAL OF GEOMETRY | 2009年 / 94卷 / 1-2期

关键词：

Ellipse; Monge's circle; Barlotti's circles; Fagnano's point;

D O I：

10.1007/s00022-009-0005-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Two new circles (denoted by Gamma(I) and Gamma(E)) are shown to be associated with any ellipse. Their analogies with two circles described by Barlotti are described. Two further new circles-denoted by Omega and F-are shown to be associated with any general point P of the ellipse. Tight relationships link the circles Omega and Gamma with the circle K (previously introduced by the present author), as well as with Monge's orthoptic circle, with Barlotti's circles and with the circles Gamma(I) and Gamma(E). In particular, the circle Omega is orthogonal to Monge's circle. A new special point of the ellipse (the point T) is described. New properties of Fagnano's point are described.

引用

页码：159 / 173

页数：15