To expand search, see Symmetry. Laterally related topics: Frieze Patterns, Plane Patterns, Bichromatic Strip Patterns, Five Fold Symmetry, Penrose Tilings, Pattern, The Regular Solids, Double Frieze Patterns, Two Sided Frieze Patterns, Rotational Symmetry Groups (Rosettes), and Bichromatic Plane Patterns.
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Loeb, A. L. The magic of the pentangle: dynamic symmetry from Merlin to Penrose. Symmetry 2: unifying human understanding, Part 1. Comput. Math. Appl. 17 (1989), no. 1-3, 33--48. (Reviewer: Marjorie Senechal.) SC: 01A99 (01A10 52-03), MR: 91a:01058a.
In this interesting and entertaining article, Merlin the magician assists Arthur and Key in exploring the secrets of dynamic symmetry (in a problem with four beetles in a square always walking towards each other), in the logarithmic spiral (the curve generated by the beetles), the golden rectangle (and its own associated spiral), and the Fibonacci numbers. The article closes with a discussion of the pentangle, which the author says "is central to the late fourteenth-century 'Sir Gawain and the Green Knight', to medieval sign theory as well as to recent research in quasi-periodic alloy crystals. The Socratic discussions here could be turned used as active learning exercises for talented students. Highly recommended. Closely related topics: England in the Middle Ages, Spirals, Proportion and the Golden Ratio, Leonardo of Pisa (Fibonacci), The Pentagram, and Education.Modify notes on this entry Modify bibliography entry Make comment on this entry
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