Abstract
That geometrical constructions were of keen interest to the ancient Greek geometers is evident from the fact that Euclid devoted two of the thirteen books of his Elements to an account of some of the constructions that had been done up to his time. In Book IV, Euclid explains how to construct an equilateral triangle, a square and the regular pentagon, hexagon, octagon, decagon and 15-gon. In Book XIII he tells how to construct the regular polyhedra, namely the tetrahedron, cube, octahedron, dodecahedron and icosahedron—which have, respectively, 4, 6, 8, 12 and 20 faces.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Berggren, J. L. “An Anonymous Treatise on the Regular Nonagon”, Journal for History of Arabic Science 5 (1981), 37–41.
Daffa, A. A. and John Stroyls, “Nasīr al-Dīn al-Tūsī’s Attempt to Prove the Parallel Postulate of Euclid”. In: Studies in the Exact Sciences in Medieval Islam. New York: Wiley, 1984.
Hogendijk, Jan P. “Greek and Arabic Constructions of the Regular Heptagon”, Archive for History of Exact Sciences 30 (1984), 197–330.
Norman, Jane and Stef Stahl, The Mathematics of Islamic Art: A Package for Teachers of Mathematics…, New York: Metropolitan Museum of Art, 1979.
Sabra, A. I. “Ibn al-Haytham’s Lemmas for Solving ‘Alhazen’s Problem’”, Archive for History of Exact Sciences 26 (1982), 299–324.
Winter, H. J. J. and W. Arafat, “Ibn al-Haitham on the Paraboloidal Focussing Mirror” and “A Discourse on the Concave Spherical Mirror of Ibn al-Haytham”. Journal of the Royal Asiatic Society of Bengal, Science 15 (No. 1) (1949), 25–40; and 16 (No. 1) (1950), 1–16, respectively.
Woepcke, F. “Analyse et Extrait d’un Recueil de Constructions Géométriques par Aboûl Wafâ”, Journal Asiatique (Ser 5), 5, Feb. –March (1855), 218–359. This contains an exposition, evidently based on a student’s notes in Persian, of Abu l-Wafā’’s fïxed-compass constructions.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag New York, Inc
About this chapter
Cite this chapter
Berggren, J.L. (1986). Geometrical Constructions in the Islamic World. In: Episodes in the Mathematics of Medieval Islam. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4608-4_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4608-4_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-40605-3
Online ISBN: 978-1-4612-4608-4
eBook Packages: Springer Book Archive