That's a huge revolution in the tiling's world: at the end of March, 2023, David Smith and his colleagues discovered a shape that allows only an aperiodic tiling of the plane. Let's look at this together.
0:00 Context
4:04 The discovery
7:36 Applications

Sources/to go further:
- The preprint on Arxiv:
https://arxiv.org/pdf/2303.10798.pdf
- Tools to go with the preprint:
https://cs.uwaterloo.ca/~csk/hat/
- Quanta magazine
https://www.quantamagazine.org/hobbyi...
- Aperiodical magazine https://aperiodical.com/2023/03/an-ap...
- David Smith blog https://hedraweb.wordpress.com
- Craig Kaplan blog https://isohedral.ca/heesch-numbers-o...

Please let us know what you think in the comments! We will be back later for a more complete video where we will see the two proofs more in detail.
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Images come from the sources above, from Wikimedia Commons or were especially made for this episode.