Written by Amelie Strupp Introduction This project aimed at providing an interactive application to visualize Root Systems and theircorresponding Weyl groups. The final version is available through the following link. Prerequisites This section introduces some important concepts by using visualizations…
Written by Lukas Schmidt, Miriam Compton and Adrian Becker Introduction During this past winter semester, we dealt with two different geometric statements: Pascal’s theorem and Poncelet’s Porism. Pascal’s theorem Let us consider six points such that if for all which…
Written by Noah Koopmann and Ingmar Lowack Due to the nature of our project, respectively the amount of subject-related text on our web application (see here), we will use the space of this blog post to talk about our work…
Written by Leon-Josip Dzojic, Matilde Sciortino, and Pirmin Kupffer In the year 1980 M. H. Freedman conjectured that every generic smooth knot in three dimensional Euclidean space has a tritangent plane, i.e., a plane tangent to three distinct points. However,…
Written by Ricardo Waibel in collaboration with Donald Youmans Topology and geometry are important concepts in mathematics and physics. Especially in theories like general relativity they have a direct impact, as the spacetime description of a system is already quite…
Written by Alassane Diagne and Ayşegül Peközsoy Möbius transformations are functions of the form \(T\colon \mathbb{C}\rightarrow\mathbb{C},\ T(z) = \frac{az+b}{cz+d}\) with \(a\), \(b\), \(c\), \(d\) complex numbers. We often associate the mapping \(T\) with the matrix \(T=\begin{pmatrix}a&b\\ c&d\end{pmatrix}\). If you look…
Written by Mouna Deubler, Yunus Sahin and Juliane Stehle During the summer term 2022, our group worked on a painting app in Hyperbolic Space of dimension two.Our goal was to create an editor for drawing, but not in the Euclidean…
Written by Ines Bultmann and Filippa Piazolo The goal of our project was to design a 2D hyperbolic game engine in p5.js using the Poincaré disk as the hyperbolic model. The inspiration for the game engine came from the arcade…
Written by Jonas Höcht, Burak Ertan und Carola Behr The famous physicist Sir Roger Penrose called the Hopf fibration “an element of the architecture of our world” – reason enough to try and visualize this remarkable map. Through the formalism…
Written by Aaron Osburg Imagine you are planning your birthday party which will take place in Heidelberg Castle. You have a lot of friends, so you are not quite sure if the inner courtyard of the castle provides enough space…
