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dc.contributor.advisorSuppose that d ≥ 2 and m are fixed. For which n is it the case that any n angles can be realised by placing m points in Rd? A simple degrees of freedom argument shows that m points in R2 cannot realise more than 2m - 4 general angles. We give a construction to show that this bound is sharp when m ≥ 5. In d dimensions the degrees of freedom argument gives an upper bound of dm−(d+12)−1dm−(2d+1)−1 general angles. However, the above result does not generalise to this case; surprisingly, the bound of 2m-4 from two dimensions cannot be improved at all. Indeed, our main result is that there are sets of 2m - 3 angles that cannot be realised by m points in any dimension.
dc.contributor.authorBalister, Pen_US
dc.contributor.authorFuredi, Zen_US
dc.contributor.authorBollobas, Ben_US
dc.contributor.authorLeader, Ien_US
dc.contributor.authorWalters, Men_US
dc.date.accessioned2016-08-26T13:12:34Z
dc.date.available2015-07-28en_US
dc.date.issued2016-07en_US
dc.date.submitted2016-07-21T15:08:33.502Z
dc.identifier.issn0021-2172en_US
dc.identifier.urihttp://qmro.qmul.ac.uk/xmlui/handle/123456789/14877
dc.description.sponsorshipThe first is partially supported by NSF grant DMS 1301614. The second author is partially supported by NSF grant DMS 1301614 and MULTIPLEX no. 317532. The third author’s research supported in part by the Hungarian National Science Foundation OTKA 104343, by the Simons Foundation Collaboration Grant #317487, and by the European Research Council Advanced Investigators Grant 267195.en_US
dc.format.extent995 - 1012en_US
dc.relation.ispartofISRAEL JOURNAL OF MATHEMATICSen_US
dc.rightsThis is a pre-copyedited, author-produced version of an article accepted for publication in Israel Journal of Mathematics following peer review. The version of record is available https://link.springer.com/article/10.1007/s11856-016-1370-1
dc.titleSubtended anglesen_US
dc.typeArticle
dc.rights.holder© Springer
dc.identifier.doi10.1007/s11856-016-1370-1en_US
pubs.author-urlhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000382866000020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=612ae0d773dcbdba3046f6df545e9f6aen_US
pubs.issue2en_US
pubs.notes12 monthsen_US
pubs.notes12 months from publication date (not yet known)en_US
pubs.publication-statusPublisheden_US
pubs.volume214en_US


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