6次元の結晶 【準結晶とペンローズタイリング】

ufolium.comは、中高から大学の数学を学べるオンラインコースです！ https://ufolium.com 無料トライアルできます！ 化学の常識を覆した結晶、「準結晶」と、非周期タイリングの数学について このような数学のアニメーション映像の作り方についても解説しています：    • 【Manim】3Blue1BrownやUfoliumの動画の作り方【第一回】   noteでも教育について発信しています: https://note.com/ufolium 公式Xアカウント： https://x.com/ufolium この動画に使われている楽曲はすべてUfolium.comから購入することができます。 Dan Shechtman, Technion - Israel Institute of Technology, (CC BY-SA 3.0), https://commons.wikimedia.org/wiki/Fi... Electron microscopy (STEM) image of a PtFe1.2 nanoparticle showing a five-fold symmetry, Ji-Hoon Jang et al., (CC BY 3.0), http://www.nature.com/srep/2013/13100... Linus Pauling in the 1940s, Oregon State University, (CC BY-SA 2.0), https://commons.wikimedia.org/wiki/Fi... Operating principle of a Transmission Electron Microscope (TEM), Jubobroff, (CC BY-SA 4.0), https://en.wikipedia.org/wiki/File:Tr... Paul J. Steinhardt, Sleepy Geek, (CC BY-SA 4.0), https://commons.wikimedia.org/wiki/Fi... Quartz, Japan Twin, Didier Descouens, (CC BY-SA 4.0), https://commons.wikimedia.org/wiki/Fi... Rock crystal, Minas Gerais - Brasil, Didier Descouens (CC BY-SA 4.0), https://commons.wikimedia.org/wiki/Fi... Roger Penrose at Festival della Scienza Oct 29 2011, Cirone-Musi, Festival della Scienza, (CC BY-SA 2.0), https://commons.wikimedia.org/wiki/Fi... Sodium chloride (salt) - crystals, Cristian V. (CC BY-SA 4.0), https://commons.wikimedia.org/wiki/Fi... Hargittai, I. (2022). Forty years of quasicrystals: a bumpy road to triumph. Structural Chemistry, 33(2), 311-314. --- Quanta Magazine, Biggest Breakthroughs in Math: 2023,    • Biggest Breakthroughs in Math: 2023   --- International Union of Crystallography's (IUCr), Report of the Executive Committee for 1991, Acta Cryst. (1992). A48, 922-946 https://journals.iucr.org/a/issues/19... Levine, D., & Steinhardt, P. J. (1984). Quasicrystals: a new class of ordered structures. Physical review letters, 53(26), 2477. Mackay, A. L. (1982). Crystallography and the Penrose pattern. Physica A: Statistical Mechanics and its Applications, 114(1-3), 609-613. Shechtman, D., Blech, I., Gratias, D., & Cahn, J. W. (1984). Metallic phase with long-range orientational order and no translational symmetry. Physical review letters, 53(20), 1951. Onoda, G. Y., Steinhardt, P. J., DiVincenzo, D. P., & Socolar, J. E. (1988). Growing perfect quasicrystals. Physical review letters, 60(25), 2653. Shechtman, D., Blech, I., Gratias, D., & Cahn, J. W. (1984). Metallic phase with long-range orientational order and no translational symmetry. Physical review letters, 53(20), 1951. Tsai, A. P., Inoue, A., & Masumoto, T. (1987). A stable quasicrystal in Al-Cu-Fe system. Japanese Journal of Applied Physics, 26(9A), L1505.