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Note on the number of obtuse angles in point sets
dc.contributor.author | Fabila-Monroy, Ruy |
dc.contributor.author | Huemer, Clemens |
dc.contributor.author | Tramuns, Eulàlia |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.date.accessioned | 2015-04-13T10:29:20Z |
dc.date.available | 2015-04-13T10:29:20Z |
dc.date.created | 2014-09 |
dc.date.issued | 2014-09 |
dc.identifier.citation | Fabila-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.issn | 0218-1959 |
dc.identifier.uri | http://hdl.handle.net/2117/27270 |
dc.description.abstract | In $1979$ 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.extent | 6 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional |
dc.subject.lcsh | Combinatorial geometry |
dc.title | Note on the number of obtuse angles in point sets |
dc.type | Article |
dc.subject.lemac | Geometria computacional |
dc.contributor.group | Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
dc.identifier.doi | 10.1142/S0218195914600012 |
dc.rights.access | Open Access |
local.identifier.drac | 15552600 |
dc.description.version | Preprint |
local.citation.author | Fabila-Monroy, R.; Huemer, C.; Tramuns, E. |
local.citation.publicationName | International journal of computational geometry and applications |
local.citation.volume | 24 |
local.citation.number | 3 |
local.citation.startingPage | 177 |
local.citation.endingPage | 182 |
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