Islamic art not only demonstrates the symbolic significance of geometric forms and their psychological, social, religious, and aesthetic functions. In addition to these purposes, Islamic art also demonstrates symmetry. Symmetry's appeal is well-known: babies tend to favor faces with symmetrical features over those with lop-sided noses or askew eyes. Although absolute symmetry is by no means a prerequisite for beauty, symmetry is usually perceived with pleasure. The Spirograph forms, explicated by Karin Deck, are sublimely symmetrical.
Spirograph hypotrochoids and epitrocoids illustrate the value of symmetry in aesthetics and they also demonstrate the prevalence of mathematics in visual art. While Spirograph patterns may not normally be considered fine art, they are nevertheless pleasing to the eye as well as the mind. Their symmetry no doubt contributes to their aesthetic appeal but Spirograph trochoids, like Islamic friezes, draw order out of chaos and reveal the prevalence of patterns throughout the universe. Moreover, Spirograph patterns illustrate the potential of mathematics to...
Spirographs are essentially idealized: their forms may not be apparent anywhere in nature but their formulas remain true, orderly, natural, and universal.
Mathematics is neither impractical nor dry. The real-world application of mathematics can demonstrate more than financial data; mathematics can explain why the frieze patterns in the Alhambra prove mesmerizing and can help a graphic designer to replicate those patterns on a smaller or larger scale. Add color to the pattern and the mathematician can create flowers as outstanding as the rose.
References
Abas, S.J. And AS Salman: Symmetries of Islamic Geometrical Patterns. Symmetry in Ethnomathematics 12(1-2). Retrieved July 29, 2006 at http://www.ethnomath.org/resources/abas2001.pdf
Deck, K. Spirograph Math. Humanistic Mathematics Journal March 1999, Vol.19, p13-17. Retrieved July 29, 2006 at http://web.stcloudstate.edu/szkeith/index11.html
Patterns, Order, and Chaos."
