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dc.contributor.authorFabila-Monroy, Ruy
dc.contributor.authorHuemer, Clemens
dc.contributor.authorTramuns, Eulàlia
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.date.accessioned2015-04-13T10:29:20Z
dc.date.available2015-04-13T10:29:20Z
dc.date.created2014-09
dc.date.issued2014-09
dc.identifier.citationFabila-Monroy, R.; Huemer, C.; Tramuns, E. Note on the number of obtuse angles in point sets. "International journal of computational geometry and applications", Setembre 2014, vol. 24, núm. 3, p. 177-182.
dc.identifier.issn0218-1959
dc.identifier.urihttp://hdl.handle.net/2117/27270
dc.description.abstractIn $1979$ Conway, Croft, Erd\H{o}s and Guy proved that every set $S$ of $n$ points in general position in the plane determines at least $\frac{n^3}{18}-O(n^2)$ obtuse angles and also presented a special set of $n$ points to show the upper bound $\frac{2n^3}{27}-O(n^2)$ on the minimum number of obtuse angles among all sets $S$. We prove that every set $S$ of $n$ points in convex position determines at least $\frac{2n^3}{27}-o(n^3)$ 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.
dc.format.extent6 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional
dc.subject.lcshCombinatorial geometry
dc.titleNote on the number of obtuse angles in point sets
dc.typeArticle
dc.subject.lemacGeometria computacional
dc.contributor.groupUniversitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.identifier.doi10.1142/S0218195914600012
dc.rights.accessOpen Access
local.identifier.drac15552600
dc.description.versionPreprint
local.citation.authorFabila-Monroy, R.; Huemer, C.; Tramuns, E.
local.citation.publicationNameInternational journal of computational geometry and applications
local.citation.volume24
local.citation.number3
local.citation.startingPage177
local.citation.endingPage182


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