Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-12829
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dc.contributor.authorBobenko, Alexander I.-
dc.contributor.authorFairley, Alexander Y.-
dc.date.accessioned2021-12-15T10:02:25Z-
dc.date.available2021-12-15T10:02:25Z-
dc.date.issued2021-02-10-
dc.identifier.issn0179-5376-
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/14056-
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-12829-
dc.description.abstractIn the projective plane, we consider congruences of straight lines with the combinatorics of the square grid and with all elementary quadrilaterals possessing touching inscribed conics. The inscribed conics of two combinatorially neighbouring quadrilaterals have the same touching point on their common edge-line. We suggest that these nets are a natural projective generalisation of incircular nets. It is shown that these nets are planar Koenigs nets. Moreover, we show that general Koenigs nets are characterised by the existence of a 1-parameter family of touching inscribed conics. It is shown that the lines of any grid of quadrilaterals with touching inscribed conics are tangent to a common conic. These grids can be constructed via polygonal chains that are inscribed in conics. The special case of billiards in conics corresponds to incircular nets.en
dc.description.sponsorshipDFG, 195170736, TRR 109: Diskretisierung in Geometrie und Dynamiken
dc.description.sponsorshipTU Berlin, Open-Access-Mittel – 2021en
dc.language.isoenen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subject.ddc510 Mathematikde
dc.subject.otherdiscrete differential geometryen
dc.subject.otherincidence theoremsen
dc.subject.otherinscribed circlesen
dc.subject.otherinscribed conicsen
dc.titleNets of Lines with the Combinatorics of the Square Grid and with Touching Inscribed Conicsen
dc.typeArticleen
tub.accessrights.dnbfreeen
tub.publisher.universityorinstitutionTechnische Universität Berlinen
dc.identifier.eissn1432-0444-
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.1007/s00454-021-00277-5en
dcterms.bibliographicCitation.journaltitleDiscrete & Computational Geometryen
dcterms.bibliographicCitation.originalpublisherplaceNew York, NYen
dcterms.bibliographicCitation.volume66en
dcterms.bibliographicCitation.pageend1400en
dcterms.bibliographicCitation.pagestart1382en
dcterms.bibliographicCitation.originalpublishernameSpringer Natureen
dcterms.bibliographicCitation.issue4en
tub.affiliationFak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik » FG Geometriede
Appears in Collections:Technische Universität Berlin » Publications

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