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Main Title: Nets of Lines with the Combinatorics of the Square Grid and with Touching Inscribed Conics
Author(s): Bobenko, Alexander I.
Fairley, Alexander Y.
Type: Article
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.
Subject(s): discrete differential geometry
incidence theorems
inscribed circles
inscribed conics
Issue Date: 10-Feb-2021
Date Available: 15-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
Sponsor/Funder: DFG, 195170736, TRR 109: Diskretisierung in Geometrie und Dynamik
TU Berlin, Open-Access-Mittel – 2021
Journal Title: Discrete & Computational Geometry
Publisher: Springer Nature
Volume: 66
Issue: 4
Publisher DOI: 10.1007/s00454-021-00277-5
Page Start: 1382
Page End: 1400
EISSN: 1432-0444
ISSN: 0179-5376
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik » FG Geometrie
Appears in Collections:Technische Universität Berlin » Publications

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