有五階對稱的晶格嗎?

20131215創刊號

作者:科里澤克 Michal Křížek、梭茨 Jakub Šolc、莎可娃 Alena Šolcová

譯者:黃俊瑋

全文閱覽

          • 作者1簡介
            科里澤克是捷克科學院數學所的教授
          • 作者2簡介
            梭茨是捷克科技大學的數學助理教授
          • 作者3簡介
            莎可娃是捷克科技大學的數學副教授
          • 譯者簡介
            黃俊瑋為師大博士班,主修數學史。譯有《數學偵探物語》,並與洪萬生教授等人合著《摺摺稱奇:初登大雅之堂的摺紙數學》。
          • 本文出處
            Notices 59 (2012) no.1, AMS。感謝三位作者提供本文圖片。
          • 延伸閱讀
            ◊ 蔡蘊明譯〈具有黃金比例的晶體〉網頁,此為2011年諾貝爾化學獎之大眾新聞稿。《臺大科學教育發展中心》http://case.ntu.edu.tw/blog/?p=9938
            ◊ 林水田〈準晶的發現〉《科學發展》472期(2012)。http://ejournal.stpi.narl.org.tw/NSC_INDEX/Journal/EJ0001/10104/10104-09.pdf
            ◊ 翁秉仁〈正多邊形拼貼〉網頁。《國科會高瞻計畫自然科學教學資源平台》http://case.ntu.edu.tw/hs/wordpress/?p=34915
          • 參考資料
            ◊ Blind and R. Blind, The semiregular polytopes, Comment. Math. Helvetici 66 (1991), 150–154.
            ◊ Brandts, S. Korotov, M. Kˇrížek, and J. Šolc, On nonobtuse simplicial partitions, SIAM Rev. 51 (2009), 317–335.
            ◊ Baranidharan, V. S. K. Balagurusamy, A. Srinivasan, E. S. R. Gopal, and V. Sasisekharan, Nonperiodic tilings in 2-dimensions: 4- and 7-fold symmetries, Phase Transition 16 (1989), 621–626.
            ◊ Bravais, Mémoire sur les systèmes formés par les points distribués régulièrement sur un plan ou dans l’espace, J. Ecole Polytech. 19 (1850), 1–128.
            ◊ Chen, R. V. Moody, and J. Patera, Noncrystallographic root systems, in Quasicrystals and Discrete Geometry (J. Patera, ed.), Fields Inst. Monographs, vol. 10, 1998, 135–178.
            ◊ S. M. Coxeter, Regular Polytopes, Methuen, London, New York, 1948, 1963.
            ◊ Engel, Geometric Crystallography: An Axiomatic Introduction to Crystallography, D. Reidel, Boston, Lancaster, Tokyo, 1986.
            ◊ Eppstein, J. M. Sullivan, and A. Üngör, Tiling space and slabs with acute tetrahedra, Comput. Geom.: Theory and Appl. 27 (2004), 237–255.
            ◊ Grünbaum, Dodecahedron and assorted parallelohedra, zonohedra, monohedra, isozonohedra and otherhedra, Math. Intelligencer 32 (2010), no. 4, 5–15.
            ◊ Grünbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman, New York, 1987.
            ◊ Guyot, News on five-fold symmetry, Nature 326 (1987), 640–641.
            ◊ C. Hales, Cannonballs and honeycombs, Notices Amer. Math. Soc. 47 (2000), 440–449.
            ◊ Koshy, Fibonacci and Lucas Numbers with Applications, Wiley, New York, 2001.
            ◊ Krafft (ed.), Johannes Kepler: Was die Welt im Innersten zusammenhält—Antworten aus Keplers Schriften mit einer Enleitung, Erläuterungen und Glossar herausgegeben von Fritz Krafft, Marix Verlag, GmbH, Wiesbaden, 2005.
            ◊ Kˇrížek and J. Šolc, From Kepler’s mosaics to five-fold symmetry (in Czech), Pokroky Mat. Fyz. Astronom. 54 (2009), 41–56.
            ◊ I. Levenshtein, On bounds for packing in ndimensional Euclidean space, Soviet Math. Dokl. 20 (1979), 417–421.
            ◊ Livio, The Golden Ratio, Headline, London, 2002.
            ◊ Masáková, J. Patera, and E. Pelantová, Inflation centers of the cut and project quasicrystal, J. Phys. A: Math. Gen. 31 (1998), 1443–1453.
            ◊ M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, J. Combin. Theory Ser. A 26 (1979), 210–214.
            ◊ Penrose, Role of aesthetics in pure and applied mathematical research, Bull. Inst. Maths. Appl. 10 (1974), 266–271.
            ◊ Sasisekharan, A new method for generation of quasi-periodic structures with n fold axes: Application to five and seven folds, Pramana 26 (1986), 283–293.
            ◊ Schulte, Tilings, in Encyclopedia of Physical Science and Technology, third ed., vol. 16, Academic Press, San Diego, 2001, 273–282.
            ◊ Šolcová, Johannes Kepler, The Founder of Celestial Mechanics (in Czech), Prometheus, Prague, 2004.
            ◊ M. Y. Sommerville, Semi-regular networks of the plane in absolute geometry, Trans. Roy. Soc. Edinburgh 41 (1905), 725–747.
            ◊ Stillwell, The story of the 120-cell, Notices Amer. Math. Soc. 48 (2001), 17–24.
            ◊ Subramaniam and K. Ramakrishnan, Rational approximants to 5-, 8-, and 7-fold two-dimensional tilings, Zeitschrift für Kristallographie 218 (2003), 590.
            ◊ Unkelbach, Die kantensymmetrischen, gleichkantigen Polyeder, Deutsche Math. 5 (1940), 306–316.
            ◊ van Leeuwen, Computing Kazhdan-Lustig- Vogan polynomials for split E8, Nieuw Archief voor Wiskunde 9 (2008), 113–116.
(Visited 13 times, 1 visits today)