This entry refers to a series of articles jointly written by Leah Wrenn Berman, Gábor Gévay, Jürgen Richter-Gebert and Serge Tabachnikov about surprising connections of Poncelet's Porism on polygons and conics and (n4)-configurations. We show that a large class of configurations exhibit a non-trivial movement via Poncelets Theorem. We provide constructions, algebraic characterisations and a general theorem that ensures movability for a wide range of (n4)-configurations. You can access the animations here.
The articles are:
"When Grünbaum meets Poncelet -- Infinite Classes of Movable n4 Configurations"
"Explicit Constructions for Poncelet Polygons"
This entry refers to an article jointly written by Aaron Montag, Tim Reinhardt and Jürgen Richter-Gebert about the possibility to transfer Euclidean ornamental patterns to hyperbolic (Cicle-Limit like) symmetric patterns. We discuss the geometry and combinatorics of the problem and also present a GPU based algorithm that performs the transofmration. At the same time this algorithm is extremely simple to implement and provides smooth and fluid transitions from one combinatorial type to another. You can access the animations here.
The article is:
"The Smooth Power of the Neandertal Method"
This entry refers to an article by Jürgen Richter-Gebert about the cobfiguration space of the equilateral pentagon. There the problem of representing the space of all configurations of five cyclically attached bars of equal length is studied. Surprisingly, it turns out that this space can be represented and structured by a hyperbolic (5,4) tiling. Alongside with the intriguing combinatorics of the situation the paper studies a way to comformally identify the paramter space of the linkage with the Poincaré disk. You can access the animations here.
The article is:
"Hyperbolic Structure of the Equilateral Pentagon"