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Illustrating Abu al-Wafā' Būzjānī: Flat Images, Spherical Constructions

Published online by Cambridge University Press:  01 January 2022

Reza Sarhangi
Reza Sarhangi*
Affiliation:
Department of Mathematics, Towson University, Towson, MD, USA
*
E-mail: [email protected]
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Abstract

This article analyzes two-dimensional images documented in the work of fourth/tenth century mathematician Abu al-Wafā' Būzjānī, which appear in his treatise, On Those Parts of Geometry Needed by Craftsmen. These images record three-dimensional tessellations of the sphere, geometric constructions, which may have served as a basis for architectural monuments and the interior design of domes in Islamic Iran. Such designs were very likely the result of collaborations among mathematicians and artists. As explained here, the construction of the icosahedron on a sphere, as presented in Būzjānī's treatise, is not mathematically correct. But the construction of the spherical dodecahedron is precise. Būzjānī's studies of the sphere as a three-dimensional form deserve further consideration as an important component in the development of mathematical thinking.

Type
Articles
Information
Iranian Studies , Volume 41 , Issue 4: Sciences, Crafts, and the Production of Knowledge: Iran and Eastern Islamic Lands (ca. 184–1153 AH/800–1740 CE) , September 2008 , pp. 511 - 523
Copyright
Copyright © Association For Iranian Studies, Inc 2008

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References

1 Sarhangi, R., Jablan, S. and Sazdanovic, R., “Modularity in Medieval Persian Mosaics: Textual, Empirical, Analytical, and Theoretical Considerations,” in Bridges: Mathematical Connections in Art, Music, and Science, Conference Proceedings, ed. by Sarhangi, Reza and Séquin, Carlo (Winfield, KS, 2004), 281–292Google Scholar. An earlier version of the present paper appeared in Bridges: Mathematical Connections in Art, Music, and Science, Conference Proceedings, ed. by Sarhangi, Reza and Sharp, John (London, 2006), 551–560Google Scholar.

2 Ghorbani, A. and Sheykhan, M. A., Būzjānī-nāmah (Tehran, 1992)Google Scholar.

3 Jazbi, S. A., trans. and ed., Hindisah Irānī: Kārbud-e Hindisah dar ‘Amal (Applied Geometry) (Tehran, 1997)Google Scholar. This book is the source of illustrations presented here (figures 2, 3, 5, 7 [left]).

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7 Whistler Alley Mathematics, Platonic Solids, http://whistleralley.com/polyhedra/platonic.htm.