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Volume 31, Number 1, pages 061-076 (2020)
https://doi.org/10.26830/symmetry_2020_1_061
FRIEZES, ROSETTES AND POLY-UNIVERSE
Eleonóra Stettner1
English version by Eszter Galambos2
1 Address: Methodological Institute, Kaposvár University, 40 Guba Sándor Street, Kaposvár, 7400 Hungary
E-mail: stettner.eleonora@gmail.com
ORCID: 0000-0002-0427-3597
2 Mathematics and English teacher trainee − Eötvös Loránd University Budapest, Hungary
E-mail: eszter.galambos.11@gmail.com
Abstract: From times immemorial, man has always been interested in symmetrical patterns and ornaments. Cave paintings, decorations of ancient ornaments; personal objects and artwork of tribal peoples are all evidence for this. Yet even more amusing to recognise not simply a symmetry but a symmetry group on a building or on a piece of textile. Friezes and rosettes – the topics of this essay – are the two simplest examples to symmetry groups. First, we give a general description of friezes and rosettes, then take a detour to folk art. Finally, we observe the possibilities of the Poly-Universe triangle and square elements from the perspective of friezes and rosettes. We are looking for tasks in the methodology book compiled for the PUSE project (Poly-Universe in School Education) that include friezes and rosettes. We examine how the task itself or the questions raised can be developed if we consider this perspective. Then we observe the possibilities, which frieze or rosette patterns can be constructed from the Poly- Universe. Is it possible to arrange all of them? Emphasizing the importance of the multidisciplinary approach is another aim for this essay. When starting off from the examination of any phenomena or problem, we always arrive at aspects of the world surrounding us. Now observations on the symmetries of the Poly-Universe set reminds us of many natural phenomena and works of art. Several examples to this are mentioned, and we also present our findings in detail, with pictures: frieze patterns of cross-stitch embroidery.
Keywords: Poly-Universe, PUSE, frieze symmetry, rosette symmetry
MSC 2010: 00A66, 97U60
References:
Bérczi, S. (1986) Escherian and non-Escherian developments of new frieze types in Hanti and old Hungarian communal art, MC Escher: Art and Science, 349-358.
Darvas, Gy. (1999) Szimmetria a tudományban és a művészetben, Magyar Tudomány, 3, [in Hungarian] Utánközlés: Retrieved from http://members.iif.hu/visontay/ponticulus/rovatok/hidverok/szimmetria_darvas.html (2020. 02. 06.)
Hargittai I. & Lengyel, Gy. (2003) A hét egydimenziós szimmetria-tércsoport magyar hímzéseken, [in Hungarian]. Retrieved from http://members.iif.hu/visontay/ponticulus/rovatok/hidverok/hargittai2.html (2020. 02. 06.)
Szász SAXON, J., Stettner, E., eds. (2019) PUSE (Poly-Universe in School Education) METHODOLOGY – Visual Experience Based Mathematics Education, Szokolya: Poly-Universe Ltd. (Publisher: Zs. Dárdai), [open access in pdf from http://poly-universe.com/puse-methodology/ 254 p. ISBN 978-615-81267-1-7]
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