Published May 22, 2017
| Version v1
Publication
Note on the number of obtuse angles in point sets
Description
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.
Abstract
Consejo Nacional de Ciencia y Tecnología (México)Abstract
Ministerio de Economía y CompetitividadAbstract
Generalitat de CatalunyaAbstract
European Science FoundationAdditional details
Identifiers
- URL
- https://idus.us.es/handle/11441/60156
- URN
- urn:oai:idus.us.es:11441/60156