6 papers
On Chasles' Quadrilateral Theorem
Leah Wrenn Berman, Jürgen Richter-Gebert
Chasles' Quadrilateral Theorem is a classical statement about four tangents to a conic that simultaneously circumscribe a circle. In its various formulations, it relates the concur…
An almost trivial observation about the icosahedron
Jürgen Richter-Gebert
We consider the incidence structure formed by the twelve pentagons given by the vertex neighborhoods of the icosahedron. Interpreting this structure purely in terms of coplanarity…
Manifold-based Proving Methods in Projective Geometry
Michael Martin Katzenberger, Jürgen Richter-Gebert
This article compares different proving methods for projective incidence theorems. In particular, a technique using quadrilateral tilings recently introduced by Sergey Fomin and Pa…
Hyperbolic Structure of the Equilateral Pentagon
Jürgen Richter-Gebert
The combinatorial structure of the realization space of the euqilateral pentagon linkage is closely related to a tiling of the hyperbolic plane by right-angled pentagons. In this c…
Explicit Constructions for Poncelet Polygons
Leah Wrenn Berman, Gábor Gévay, Jürgen Richter-Gebert +1
We study the geometric structure of Poncelet -gons from a projective point of view. In particular we present explicit constructions of Poncelet -gons for certain and deri…
When Grünbaum meets Poncelet -- Infinite Classes of Movable Configurations
Leah Wrenn Berman, Gábor Gévay, Jürgen Richter-Gebert +1
We study relations between incidence configurations and the classical Poncelet Porism. Poncelet's result studies two conics and a sequence of points and lines that inscribe…