On Holditch’s theorem-Reference-Cited by-同舟云学术

On Holditch’s theorem

Published:2020-04-29 Issue:2 Volume:111 Page:
ISSN:0047-2468
Container-title:Journal of Geometry
language:en
Short-container-title:J. Geom.

Author:

Cieślak Waldemar,Martini Horst,Mozgawa Witold

Abstract

AbstractIn this paper we present a certain modification of the Holditch construction. This construction allows to consider a geometric family of pairs of ring domains. It is proved that the ratio of areas of ring domains of each pair belonging to this family is constant. Problems on extremal chords of constant length sliding around a given oval with both endpoints on it are also considered.

Funder

Maria Curie-Sklodowska University in Lublin

Publisher

Springer Science and Business Media LLC

Subject

Geometry and Topology

Link

https://link.springer.com/content/pdf/10.1007/s00022-020-00536-5.pdf

Reference18 articles.

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3. Broman, A.: Holditch’s theorem is somewhat deeper than Holditch thought in 1858. Nordisk Mathematisk Tidskrift 27, 89–100 (1979). (in Swedish)

4. Broman, A.: Holditch’s theorem. Math. Mag. 54, 99–108 (1981)

5. Cieślak, W., Koshi, S., Zaja̧c, J.: On integral formulas for convex domains. Acta Math. Hungar. 62, 277–283 (1993)

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