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Characterization of Extremal Antipodal Polygons

Aichholzer, O. ; Caraballo, L. E. ; Díaz-Báñez, J. M. ; Fabila-Monroy, R. ; Ochoa, C. ; Nigsch, P.

Graphs and combinatorics, 2015-03, Vol.31 (2), p.321-333 [Periódico revisado por pares]

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Título:
Characterization of Extremal Antipodal Polygons
Autor: Aichholzer, O. ; Caraballo, L. E. ; Díaz-Báñez, J. M. ; Fabila-Monroy, R. ; Ochoa, C. ; Nigsch, P.
Assuntos: Algorithms ; Combinatorial analysis ; Combinatorics ; Computing time ; Engineering Design ; Geometry ; Graphs ; Mathematics ; Mathematics and Statistics ; Original Paper ; Polygons ; Texts
É parte de: Graphs and combinatorics, 2015-03, Vol.31 (2), p.321-333
Notas: ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
Descrição: Let S be a set of 2 n points on a circle such that for each point p ∈ S also its antipodal (mirrored with respect to the circle center) point p ′ belongs to S . A polygon P of size n is called antipodal if it consists of precisely one point of each antipodal pair ( p , p ′ ) of S . We provide a complete characterization of antipodal polygons which maximize (minimize, respectively) the area among all antipodal polygons of S . Based on this characterization, a simple linear time algorithm is presented for computing extremal antipodal polygons. Moreover, for the generalization of antipodal polygons to higher dimensions we show that a similar characterization does not exist.
Editor: Tokyo: Springer Japan
Idioma: Inglês

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