Convexly independent subsets of the Minkowski sum of planar point sets.

Eisenbrand, Friedrich; Pach, János; Rothvoß, Thomas; Sopher, Nir B.

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Another abstraction of the Erdős-Szekeres happy end theorem.

Alon, Noga, Chiniforooshan, Ehsan, Chvátal, Vašek, Genest, François (2010)

The Electronic Journal of Combinatorics [electronic only]

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Large convexly independent subsets of Minkowski sums.

Swanepoel, Konrad J., Valtr, Pavel (2010)

The Electronic Journal of Combinatorics [electronic only]

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The isoperimetric inequality for a pentagon in $E_{3}$ and its generalization in $E_{n}$ space

Milada Kočandrlová (1982)

Časopis pro pěstování matematiky

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Parallelograms inscribed in a curve having a circle as π/2-isoptic

Andrzej Miernowski (2008)

Annales UMCS, Mathematica

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Jean-Marc Richard observed in [7] that maximal perimeter of a parallelogram inscribed in a given ellipse can be realized by a parallelogram with one vertex at any prescribed point of ellipse. Alain Connes and Don Zagier gave in [4] probably the most elementary proof of this property of ellipse. Another proof can be found in [1]. In this note we prove that closed, convex curves having circles as π/2-isoptics have the similar property.

Piecewise Convex Curves and their Integral Representation

Nedelcheva, M. D. (2006)

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2000 Mathematics Subject Classification: 52A10. A convex arc in the plane is introduced as an oriented arc G satisfying the following condition: For any three of its points c1 < c2 < c3 the triangle c1c2c3 is counter-clockwise oriented. It is proved that each such arc G is a closed and connected subset of the boundary of the set FG being the convex hull of G. It is shown that the convex arcs are rectifyable and admit a representation in the natural parameter by the...