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Displaying similar documents to “On the Impossibility of one Ruler-and-Compass Construction”

Morse index of a cyclic polygon

Gaiane Panina, Alena Zhukova (2011)

Open Mathematics

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It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper we give an explicit formula of the Morse index for the signed area of a cyclic configuration. We show that it depends not only on the combinatorics of a cyclic configuration, but also on its metric properties.

Approximating the MaxMin and MinMax Area Triangulations using Angular Constraints

Mark Keil, J, Vassilev, Tzvetalin (2010)

Serdica Journal of Computing

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* A preliminary version of this paper was presented at XI Encuentros de Geometr´ia Computacional, Santander, Spain, June 2005. We consider sets of points in the two-dimensional Euclidean plane. For a planar point set in general position, i.e. no three points collinear, a triangulation is a maximal set of non-intersecting straight line segments with vertices in the given points. These segments, called edges, subdivide the convex hull of the set into triangular regions called...