Geometriae Dedicata

, Volume 60, Issue 2, pp 145–151

On the products of cross-ratios on diagonals of polygons

  • Joseph Zaks

DOI: 10.1007/BF00160619

Cite this article as:
Zaks, J. Geom Dedicata (1996) 60: 145. doi:10.1007/BF00160619


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 δ(P), such that the product of the cross-rations on the diagonals of P is equal to the product of the corresponding cross-ratios on the diagonals of δ(P).

Mathematics Subject Classifications (1991)

51A05 51M15 51N15 

Key words

Polygons Grünbaum conjecture 

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Joseph Zaks
    • 1
  1. 1.University of HaïfaHaïfaIsrael

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