Geometriae Dedicata

, Volume 60, Issue 2, pp 145-151

First online:

On the products of cross-ratios on diagonals of polygons

  • Joseph ZaksAffiliated withUniversity of Haïfa

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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