Symmetry Orbits: When Artists and Mathematicians Disagree

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Darrah Chavey: Symmetry Orbits: When Artists and Mathematicians Disagree. In: Bridges 2011. Pages 337–344



In many examples of repeating patterns in the art of various cultures, the use of symmetries to analyze those patterns does a good job of capturing the repetition intended by the artist. In other cases, however, the artist uses precise forms of repetition that are not well modeled by mathematical symmetries. The analysis of the orbits of motifs under the action of the symmetry group both reveals situations where this happens, and gives us direction as to what else is needed to model the artists’ apparent intent. The ways in which the art of different cultures need different types of extensions of symmetry ideas reveals structural differences in the design art of those cultures, and hence in their ethnomathematics.

Extended Abstract


Used References

[1] Marcia Ascher, Ethnomathematics, a Multicultural View of Mathematical Ideas, Brooks-Cole, 1991.

[2] Szaniszló Bérczi, “New Curie-type and Coxeter-type composite and colored plane symmetry patterns in the ancient arts of Eurasia,” in Symmetry: Culture and Science, 20(1-4), 161-176, 2009.

[3] Christopher Donnan, Moche Portraits from Ancient Peru, Univ. of Texas Press, 2004.

[4] Branko Grünbaum & G. C. Shephard, Tilings and Patterns, W. H. Freeman, 1987.

[5] Augustus Hamilton, Maori Art, The New Zealand Institute, Wellington, New Zealand, 1896-1901.

[6] Alfred Kroeber & Donald Collier, The Archaeology and Pottery of Nazca, Peru, Altamira, 1998.

[7] Dorothy Menzel, John Rowe, & Lawrence Dawson, The Paracas Pottery of Ica, Univ. of Calif, 1964.

[8] Dorothy K. Washburn & Donald W. Crowe, Symmetries of Culture, Univ. of Washington, 1988.


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