From Friezes to Quasicrystals: A History of Symmetry Groups

Franka Miriam Brückler () and Vladimir Stilinović ()
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Franka Miriam Brückler: University of Zagreb, Department of Mathematics, Faculty of Science
Vladimir Stilinović: University of Zagreb, Department of Chemistry, Faculty of Science

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 1823-1863 from Springer

Abstract: Abstract Even if, since many thousands of years, humans were fascinated by symmetry, which is reflected in many preserved ornaments on buildings, paintings, pottery, etc., the mathematical study of symmetrical patterns is just a few hundred years old. In fact, until the nineteenth century, when it received an impulse from crystallography, no systematical approaches were developed. In this chapter, we follow the history of (Euclidean) symmetry from its first appearances and connections with art, over geometric classifications by nineteenth-century crystallographers, the coalescence of this crystallographic-geometrical approach with theory of groups in the second part of the nineteenth century, until various twentieth-century generalizations to symmetry groups in higher dimensions, magnetic, and colored groups.

Keywords: Euclidean symmetry; Mathematical crystallography; History of group theory; Point groups; Space groups; Color groups; Magnetic groups (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-40846-5_132

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DOI: 10.1007/978-3-031-40846-5_132

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