## Contact Geometries – Introducing Knoty

Written by Stanislaus Stein The goal of this Python Module is to provide an interactive framework for the visualization of Legendre knots. It generates interactive 3D plots of Legendre knots and contact structures. The final result is an interactive plot…

## Wallpaper groups: The reason why Heidelberg is better than Granada

Written by: Caroline Bornmann, Sebastian Grafe, Johannes Kamlage The reason why Heidelberg is better than Granada Granada in Spain. Roughly 230.000 habitants and a beloved holiday destination for many tourists. But why exactly is this beautiful piece of land in…

## Math Board Game: Museum Heist

Written by: Julia Bulitta, Alina Czasch, Hanna Heer, Tadeus Pindl, Fabian Walliser 1. Introduction During this past summer semester, we dealt with the task to construct a game which has mathematical knowledge. There are already many games that have mathematical…

## Reconstruction of Badr al-Din al-Ayni Mihrab

Written by Almoatasembellah Haggag Abstract The Mihrab (a concave niche situated in the wall of a mosque facing Mecca. [3]) of the 15th-century Badr al-Dın al-Aynı Madrasa in Cairo, renowned for its significance and uniqueness in the medieval city of…

## Reinforcement Learning for Finding Counterexamples in Graph Theory

Written by Karl Schamel, Cheni Yang, and Hugo Introduction Many conjectures in graph theory remain open due to the hardness of giving an explicit proof, but they are also easy to be disproven by only a constructive example. Inspired by…

## Generating Victory Boogie Woogie by Piet Mondrian

Written by: Bastian Hirschfeld, Heidi Rhodes James, Arjan Siddhpura, Ioana Todosi In the past semester we have developed a website that shows computer generated compositions in the style of Victory Boogie Woogie which is Mondrian’s last and unfinished work. To…

## Theorem Proving with Lean

Written by: Nikita Grimm, Sebastian Meier, Frederick VandermoetenA hosted version of the app can be found at Starting our project, we embarked on our journey with the Natural Number Game (NNG) to learn about the syntax of Lean 3. We also…

## Continuous Cellular Automata

In a Cellular Automata, we simulate a grid of cells. For each cell, we can calculate its upcoming state based on its previous state. A very famous example of such a system is Conway’s Game of Life. In the Game…

## 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…