Yvonne Dold-Samplonius
Ruprecht-Karls-Universität Heidelberg
Institute of Mathematics
Im Neuenheimer Feld 288
D-69120 Heidelberg GERMANY    

Silvia Harmsen
Ruprecht-Karls-Universität Heidelberg
Interdisciplinary Center for Scientific Computing
Im Neuenheimer Feld 368
D-69120 Heidelberg GERMANY

The Timurid astronomer and mathematician Ghiyath al-Din al Kashi (d.1429) ranks among the greatest mathematicians and astronomers in the Islamic world. His talent to optimize a problem let him appear as the first modern mathematician.
The Key of Arithmetic, one of his major works, is intended for everyday use. The most extensive part of this work is Book IV, "On Measurements". The last chapter, "Measuring Structures and Buildings", is really written for practical purposes. Al- Kashi uses geometry as a tool for his calculations, not for constructions. Besides arches, vaults, and qubbas (domes), al- Kashi calculates here the surface area of a muqarnas, to say, he establishes approximate values for such a surface.

Muqarnas is the Arabic word for stalactite vault, an architectural ornament developed around the middle of the tenth century in north eastern Iran and almost simultaneously, but apparently independently, in central North Africa. A muqarnas is a three-dimensional architectural decoration composed of nichelike elements arranged in tiers. The two-dimensional projection of a muqarnas vault consists of a small variety of simple geometrical elements, as seen in Figure 1.


Figure 1: Part of a muqarnas with its projection.

In the scope of our three year project "Computer Reconstruction of Muqarnas", we are analyzing muqarnas and building up a data-base for these constructions. At the end of our project the computer should be able to show us a three-dimensional vault of the requested time, region, and style based on a two dimensional plan. In case the vault has partly collapsed in time, the computer should give us ideas how to restore the vault.

ABOUT THE AUTHORS
This email address is being protected from spambots. You need JavaScript enabled to view it. is guest member of the Center for Scientific Computing (IWR) of the University of Heidelberg, where she directed the video "Qubba for al-Kashi", showing al-Kashi's geometrical constructions for determining the volumes of domes and arches. With her team she is now working on a three-year Muqarnas (stalactite vaults) project sponsored by the German Ministry of Education and Research (BMBF). With international cooperation they are developing a computer method to create virtual muqarnas based on old plans, like the Topkapi Scroll, or to make suggestions for restoring partly collapsed muqarnas, like the Friday Mosque at Varamin, Iran.
She has edited, with J.W. Dauben and M. Folkerts as co-editors, the proceedings of the conference "Transmission of Mathematics", held in May 2000 at the Rockefeller Center in Bellagio, Italy. These proceedings, From China to Paris: 2000 Years of Mathematical Transmission, have appeared in 2002 at Steiner Verlag, Stuttgart.
On the occasion of the International Congress on Ghiyath al-Din Kashani, held at Kashan, Iran, in November 2000, she was made an honorary citizen of the town of Kashan. She is a corresponding member of the International Academy for History of Science. Her webpage can be found at http://www.iwr.uni-heidelberg.de/~Yvonne.Dold-Samplonius/

This email address is being protected from spambots. You need JavaScript enabled to view it., born in 1978 in Ermelo (the Netherlands), started studying mathematics in 1996 at the Utrecht University. There she received in 2001 cum laude her diploma in the field of Algebra and Geometry. Since 2002 she is working on Computer Reconstructions of
Muqarnas as a Ph.D.-student at the IWR, Interdisciplinary Center for Scientific Computing, University of Heidelberg.

The correct citation for this paper is:
Yvonne Dold-Samplonius and Silvia Harmsen, "Muqarnas, Construction and Reconstruction", pp. 69-77 in Nexus V: Architecture and Mathematics, ed. Kim Williams and Francisco Delgado Cepeda, Fucecchio (Florence): Kim Williams Books, 2004.