On the products of cross-ratios on diagonals of polygons
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 wordsPolygons Grünbaum conjecture
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- 1.Grünbaum, B.: Quadrangles, pentagons and computers, Geombinatorics 3 (1993), 4–9.Google Scholar
- 2.Grünbaum, B.: Quadrangles, pentagons and computers, revisited, Geombinatorics 4 (1994), 11–16.Google Scholar
- 3.Moran, M.: About a conjecture of Schoenberg on nested polygons, in C. Alsina et al. (eds) European Conference on Iteration Theory (ECIT 87), Caldes de Malavella, Spain, Sept. 1987, World Scientific, Washington, D.C., 1990, pp. 295–305.Google Scholar
- 4.Schwartz, R.: The pentagram map, Exper. Math. 1 (1992), 71–81.Google Scholar