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The Use of Cubic Equations in Islamic Art and Architecture

In: Architecture and Mathematics from Antiquity to the Future

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  • Alpay Özdural

    (Middle Eastern Technical University)

Abstract

An anonymous Persian work on ornamental geometry, On interlocks of similar or complementary figures, appears to have been compiled by a scribe at a series of meetings between mathematicians and artisans. This unusual document, which contains 68 geometric constructions mostly with verbal explanations, can be dated by internal evidence to ca. 1300. Some of those constructions display the highest advancements attained by Muslim mathematicians, and thus represent the intimate link between theory and praxis that created the intriguing and awe-inspiring ornamental patterns. Three constructions are the solutions to problems that require cubic equations. At the time, mathematicians solved cubic equations by means of conic sections, but such solutions were only for demonstration purposes with no practical application. These three constructions in Interlocks of Figures are the cases of “moving geometry,” that is, mechanical procedures that are equivalent to the solutions for cubic equations.

Suggested Citation

  • Alpay Özdural, 2015. "The Use of Cubic Equations in Islamic Art and Architecture," Springer Books, in: Kim Williams & Michael J. Ostwald (ed.), Architecture and Mathematics from Antiquity to the Future, edition 127, chapter 0, pages 467-481, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-00137-1_32
    DOI: 10.1007/978-3-319-00137-1_32
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