6 citations · 18 across the 8 of their papers we have counts for
8 papers
The Smooth Power of the "Neandertal Method"
Aaron Montag, Tim Reinhardt, Jürgen Richter-Gebert
We describe an algorithmic method to transform a Euclidean wallpaper pattern into a Circle Limit-style picture à la Escher. The design goals for the method are to be mathematically…
Bringing Together Dynamic Geometry Software and the Graphics Processing Unit
Aaron Montag, Jürgen Richter-Gebert
We equip dynamic geometry software (DGS) with a user-friendly method that enables massively parallel calculations on the graphics processing unit (GPU). This interplay of DGS and G…
Cayley-Bacharach Formulas
Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels
The Cayley-Bacharach Theorem states that all cubic curves through eight given points in the plane also pass through a unique ninth point. We write that point as an explicit rationa…
Geometry of Numerical Complex Time Integration
Thorsten Orendt, Jürgen Richter-Gebert, Michael Schmid
We are studying Runge-Kutta methods along complex paths of integration from a geometric point of view. Thereby we derive special complex time grids, which applied to the problem of…
Every non-Euclidean oriented matroid admits a biquadratic final polynomial
Komei Fukuda, Sonoko Moriyama, Hiroki Nakayama
Richter-Gebert proved that every non-Euclidean uniform oriented matroid admits a biquadratic final polynomial. We extend this result to the non-uniform case.
First steps in tropical geometry
Jürgen Richter-Gebert, Bernd Sturmfels, Thorsten Theobald
Tropical algebraic geometry is the geometry of the tropical semiring . Its objects are polyhedral cell complexes which behave like complex algebraic varieties.…