On the products of cross-ratios on diagonals of polygons

Joseph Zaks

doi:10.1007/BF00160619

On the products of cross-ratios on diagonals of polygons

Joseph Zaks

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The purpose of this paper is to establish a conjecture of B. Grünbaum, which states that in every n-polygon P in the plane, n ≥ 5, some diagonals intersect in a pattern that defines a new n-polygon 6 (P), such that the product of the cross-ratios on the diagonals of P is equal to the product of the corresponding cross-ratios on the diagonals of δ(P).

Original language	English
Pages (from-to)	145-151
Number of pages	7
Journal	Geometriae Dedicata
Volume	60
Issue number	2
DOIs	https://doi.org/10.1007/BF00160619
State	Published - 1996

Keywords

Grünbaum conjecture
Polygons

ASJC Scopus subject areas

Geometry and Topology

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10.1007/BF00160619

Cite this

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abstract = "The purpose of this paper is to establish a conjecture of B. Gr{\"u}nbaum, which states that in every n-polygon P in the plane, n ≥ 5, some diagonals intersect in a pattern that defines a new n-polygon 6 (P), such that the product of the cross-ratios on the diagonals of P is equal to the product of the corresponding cross-ratios on the diagonals of δ(P).",

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On the products of cross-ratios on diagonals of polygons

Abstract

Keywords

ASJC Scopus subject areas

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