# Category Proseminar/Seminar

## Political Geometry

A comprehensive study on cooperation and cosponsoring in the US Senate Written by Ayşegül Peközsoy, Leo Späth, and Klaus Stier Political Background The United States of America is a federal republic with a presidential system, meaning that the executive branch…

## Physical Graph Layout in Hyperbolic Space

Written by David Li, Anna Roth Introduction Visual graph layouts are a nice tool to quickly spot symmetries and other structures on graphs. As common graph layout tools, such as Gephi, can only layout graphs in Euclidean space, our goal…

## Root Systems and their Weyl Groups

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…

## Pascal’s theorem and Poncelets Porism

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…

## Quasicrystals

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…

## Indra’s Pearls

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…

## Mobius Paint

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…

## Hyperbolic Game Engine

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…

## Visualizing the Hopf fibration

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…

## Escher in 3D

Written by Helen Freytag and Ronya Ramrath. Inspired by Escher’s experimentation with hyperbolic art (and driven by the tempting availability of 3D printers in the clearly very well-funded experimental geometry lab), this project was concerned with extrapolating and printing the…