全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

Enclosing Ellipses by Folding Disks

DOI: 10.4236/am.2022.132012, PP. 147-162

Keywords: Straight Line, Perpendicular Bisector, Linear System, Determinant, Point of Intersection, Gardner Ellipse, Bidirectional Folding

Full-Text   Cite this paper   Add to My Lib

Abstract:

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.

References

[1]  Gorkin, P. and Shaffer, A. (2021) Making Ellipses by Folding Disks. Mathematics Magazine, 94, 53-58.
https://doi.org/10.1080/0025570X.2021.1849923
[2]  Poncelet, J.V. (1865-1866) Traité des propriétés projectives des figures: ouvrage utile à qui s’occupent des applications de la géometrié descriptive et d’opérations géométriques sur le terrain. Vols. 1-2, 2nd Edition, Gauthier-Villars, Paris.
[3]  Daepp, U., Gorkin, P. and Mortini, R. (2002) Ellipses and Finite Blaschke Products. The American Mathematical Monthly, 109, 785-795.
https://doi.org/10.1080/00029890.2002.11919914
[4]  Gardner, M. (1995) New Mathematical Diversions. Revised Edition, Mathematical Association of America, Washington DC.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133