Nets of Lines with the Combinatorics of the Square Grid and with Touching Inscribed Conics

Bobenko, Alexander I.; Fairley, Alexander Y.

Nets of Lines with the Combinatorics of the Square Grid and with Touching Inscribed Conics

dc.contributor.author	Bobenko, Alexander I.
dc.contributor.author	Fairley, Alexander Y.
dc.date.accessioned	2021-12-15T10:02:25Z
dc.date.available	2021-12-15T10:02:25Z
dc.date.issued	2021-02-10
dc.description.abstract	In 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.sponsorship	DFG, 195170736, TRR 109: Diskretisierung in Geometrie und Dynamik	en
dc.description.sponsorship	TU Berlin, Open-Access-Mittel – 2021	en
dc.identifier.eissn	1432-0444
dc.identifier.issn	0179-5376
dc.identifier.uri	https://depositonce.tu-berlin.de/handle/11303/14056
dc.identifier.uri	http://dx.doi.org/10.14279/depositonce-12829
dc.language.iso	en	en
dc.rights.uri	https://creativecommons.org/licenses/by/4.0/	en
dc.subject.ddc	510 Mathematik	de
dc.subject.other	discrete differential geometry	en
dc.subject.other	incidence theorems	en
dc.subject.other	inscribed circles	en
dc.subject.other	inscribed conics	en
dc.title	Nets of Lines with the Combinatorics of the Square Grid and with Touching Inscribed Conics	en
dc.type	Article	en
dc.type.version	publishedVersion	en
dcterms.bibliographicCitation.doi	10.1007/s00454-021-00277-5	en
dcterms.bibliographicCitation.issue	4	en
dcterms.bibliographicCitation.journaltitle	Discrete & Computational Geometry	en
dcterms.bibliographicCitation.originalpublishername	Springer Nature	en
dcterms.bibliographicCitation.originalpublisherplace	New York, NY	en
dcterms.bibliographicCitation.pageend	1400	en
dcterms.bibliographicCitation.pagestart	1382	en
dcterms.bibliographicCitation.volume	66	en
tub.accessrights.dnb	free	en
tub.affiliation	Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Geometrie	de
tub.affiliation.faculty	Fak. 2 Mathematik und Naturwissenschaften	de
tub.affiliation.group	FG Geometrie	de
tub.affiliation.institute	Inst. Mathematik	de
tub.publisher.universityorinstitution	Technische Universität Berlin	en

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