Enclosing Ellipses by Folding Disks  

作　　者：Peter Paul Klein Peter Paul Klein(University of Technology Clausthal, Clausthal-Zellerfeld, Germany)

机构地区：[1]University of Technology Clausthal, Clausthal-Zellerfeld, Germany

出　　处：《Applied Mathematics》2022年第2期147-162,共16页应用数学（英文）

摘　　要：Ellipses can be constructed by folding disks. These folds are forming an envelope of tangents to the ellipse. In the paper of Gorkin and Shaffer, it was shown that the ellipse constructed by folding can be circumscribed by an arbitrary triangle of tangents, the vertices of which are lying on the circumference of the disk. They offered two non-elementary methods of proof, one using Poncelet’s Theorem, the other employing Blaschke products. In this paper, it is the intention to present an elementary proof by means of analytic geometry.Ellipses can be constructed by folding disks. These folds are forming an envelope of tangents to the ellipse. In the paper of Gorkin and Shaffer, it was shown that the ellipse constructed by folding can be circumscribed by an arbitrary triangle of tangents, the vertices of which are lying on the circumference of the disk. They offered two non-elementary methods of proof, one using Poncelet’s Theorem, the other employing Blaschke products. In this paper, it is the intention to present an elementary proof by means of analytic geometry.

关 键 词：Straight Line Perpendicular Bisector Linear System DETERMINANT Point of Intersection Gardner Ellipse Bidirectional Folding 

分 类 号：O175[理学—数学]