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# The Seven-Circle-Theorem
# The Seven Circle Theorem

This repository contains the source code for a video about the proof of the Seven-Circle-Theorem by [Drach und Schwartz](https://arxiv.org/pdf/1911.00161.pdf).
This repository contains the source code for a video about the proof of the Seven Circle Theorem by [Drach and Schwartz](https://arxiv.org/pdf/1911.00161.pdf).
The video was created using [manim](https://github.com/ManimCommunity/manim).

The video is uploaded to [YouTube](https://youtu.be/flR3e5Cc2G4). The video is in German but English subtitles are available as well.
The video is uploaded to YouTube. The video is available in [English](https://youtu.be/m9v0h2ibYpo) and in [German](https://youtu.be/flR3e5Cc2G4).

## 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.
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.

[![The Seven-Circle-Theorem](thumbnail.png)](https://youtu.be/flR3e5Cc2G4)
[![The Seven Circle Theorem](thumbnail.png)](https://youtu.be/m9v0h2ibYpo)

## Acknowledgments

[`tessellation_klein.png`](tessellation_klein.png) and [`tessellation_poincare.png`](tessellation_poincare.png) are made using the [Hyperbolic Tessellation program](https://dmitrybrant.com/2007/01/24/hyperbolic-tessellations) by [Dmirty Brant](https://github.com/dbrant).

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