The Seven Circle Theorem

This repository contains the source code for a video about the proof of the Seven Circle Theorem by Drach and Schwartz. The video was created using manim.

The video is uploaded to YouTube. The video is available in English and in German.

Theorem

For every chain $H_1, \ldots, H_6$ of consequently touching circles inscribed in and touching the unit circle, the three main diagonals of the hexagon comprised of the points at which the chain touches the unit circle, intersect at a common point.

Acknowledgments

tessellation_klein.png and tessellation_poincare.png are made using the Hyperbolic Tessellation program by Dmirty Brant.

Development

Prerequisites

For development, you need to install pixi as well as TeXLive.

On macOS, you can do this via Homebrew:

brew install pixi
brew install mactex-no-gui

On Ubuntu, you can do this as follows:

sudo apt install texlive-full
curl -fsSL https://pixi.sh/install.sh | bash

On Windows, you can use the TeX Live installer and install pixi as follows:

winget install prefix-dev.pixi

Rendering

To render the videos, run

pixi run 4k-render-all