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First aperiodic tile in history! (March 2023). Let's talk about this discovery and its field of mathematics between combinatorics and geometry: the study of plane tilings. Summary: 0:00 Intro 1:02 Periodic tilings 1:45 Non-periodic tilings 4:10 Aperiodic tiles 8:27 The first aperiodic tile 14:49 Heesch number 16:37 A continuum of aperiodic tiles 17:36 A demonstration 22:18 Curiosities and questions 23:10 Outro Find Passe-science on Tipeee, Twitter and Facebook: https://www.tipeee.com/passe-science / thomascabaret84 / passescience.youtube Link to the discovery: https://cs.uwaterloo.ca/~csk/hat/ On the same subject, another FR channel: • An aperiodic pattern! Penrose tiling: https://en.wikipedia.org/wiki/Penrose... Short publication on Robinson tiles: https://lipn.univ-paris13.fr/~ferniqu... Publication on crab and trilobite tiles: https://arxiv.org/abs/1608.07167 Publications on various tilings: https://arxiv.org/abs/1606.04459 Examples of Heesch numbers: https://isohedral.ca/heesch-numbers-o... https://faculty.washington.edu/cemann... https://link.springer.com/article/10.... The tile capable of surrounding itself with only 2 copies of itself: https://faculty.washington.edu/cemann... Music: Hi-tech corporate - The Right Music for video https://www.musicscreen.org/Royalty-f... Also Sprach Zarathustra (Richard Strauss) Kevin MacLeod - Youtube Audio Library Brittle Rille Reunited - Youtube Audio Library Frost Waltz - Youtube Audio Library Groove Grove - Youtube Audio Library Two of us - Youtube Audio Library Flutey Funk - Youtube Audio Library