Presentation
Note on the number of obtuse angles in point sets
Author/s | Fabila Monroy, Ruy
Huemer, Clemens Tramuns Figueras, Eulàlia |
Editor | Díaz Báñez, José Miguel
Garijo Royo, Delia Márquez Pérez, Alberto Urrutia Galicia, Jorge |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II |
Publication Date | 2013 |
Deposit Date | 2017-05-22 |
Published in |
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Abstract | In 1979 Conway, Croft, Erd\H{o}s and Guy proved that every set SS of nn points in general position in the plane determines at least n3/18−O(n2) obtuse angles and also presented a special set of nn points to show the upper ... In 1979 Conway, Croft, Erd\H{o}s and Guy proved that every set SS of nn points in general position in the plane determines at least n3/18−O(n2) obtuse angles and also presented a special set of nn points to show the upper bound 2n3/27−O(n2) on the minimum number of obtuse angles among all sets SS. We prove that every set SS of nn points in convex position determines at least 2n327−o(n3)2n327−o(n3) obtuse angles, hence matching the upper bound (up to sub-cubic terms) in this case. Also on the other side, for point sets with low rectilinear crossing number, the lower bound on the minimum number of obtuse angles is improved. |
Project ID. | 153984
MTM2012-30951 2009SGR1040 MTM2011-28800-C02-01 |
Citation | Fabila Monroy, R., Huemer, C. y Tramuns Figueras, E. (2013). Note on the number of obtuse angles in point sets. En XV Spanish Meeting on Computational Geometry, Sevilla. |
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