Polyhedral Painting with Group Averaging

Autor/inn/en	Farris, Frank A.; Tsao, Ryan
Titel	Polyhedral Painting with Group Averaging
Quelle	In: PRIMUS, 26 (2016) 4, S.312-324 (13 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1051-1970
DOI	10.1080/10511970.2015.1110218
Schlagwörter	Undergraduate Students; Art Activities; Mathematical Concepts; Photography; Geometry; Geometric Concepts; Painting (Visual Arts); Teaching Methods; Mathematical Applications; Interdisciplinary Approach; Integrated Activities; Cluster Grouping; California + Suchen Sie Ihr Suchwort? Künstlerische Tätigkeit; Fotografie; Geometrie; Elementare Geometrie; Malerei; Teaching method; Lehrmethode; Unterrichtsmethode; Angewandte Mathematik; Innermathematische Anwendung; Fächerübergreifender Unterricht; Fächerverbindender Unterricht; Interdisziplinarität; Integrierender Unterricht; Eingruppierung; Kalifornien
Abstract	The technique of "group-averaging" produces colorings of a sphere that have the symmetries of various polyhedra. The concepts are accessible at the undergraduate level, without being well-known in typical courses on algebra or geometry. The material makes an excellent discovery project, especially for students with some background in computer science; indeed, this is where the authors first worked through the material, as teacher and student, producing a previously unseen type of artistic image. The process uses a photograph as a palette, whose colors and textures appear in kaleidoscopic form on the surface of a sphere. We depict tetrahedral, octahedral, and icosahedral symmetries, with and without mirrors, along with the source photograph for comparison. We also describe a method to make images with color-reversing symmetry. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01