## 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…

## 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…

## Hyperbolic Ping-Pong Game

Written by Isabel Giray, Karina Kniel and Phil Neitzel. The goal of this project is to give an intuitive way of understanding the hyperbolic space. Inspired by the classic Ping-Pong game which is played in an Euclidean setting, the hyperbolic…

## Tessellations of the Poincaré Disk

Written by Mara-Eliana Popescu. If asked to think of a tiling of the Euclidean Plane, surely many of us would imagine the pattern on a chessboard and perhaps some might try picturing a Penrose tiling. Such tessellations are well-known beyond…