# Ricardo Waibel

## 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…

## 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…

## Rolling Knots

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,…

## Visualizing Topology and Geometry with a Physics Connection

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…

## 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…

## Planimeters

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…

## 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…

## Delta-Slim Triangles

Written by Deniz Aydın and Simon Heidrich. It is easy to imagine how spherical triangles are “fatter” than Euclidean ones. Just like this, hyperbolic triangles look slimmer in comparison. Gromov used this property to generalize hyperbolic spaces. Imagine δ-neighborhoods of…