muqarnas - English version
Muqarnas mark one of the most remarcable features of Islamitische Architecture. In it curved surfaces as domes, half domes and portals are decorated by an astonishing combination of curved facets. For a layman it's incomprehensible how one can conceive such a spatial construction. On a second look muqarnas have much in common with tilings and the concepts of symmetry in 2D. In this book you discover the link between a 2D and a 3D-look and you can look in detail to some nice examples. Finally fiind links to other fascinating material on muqarnas. I worked together with Henk Hietbrink in creating GeoGebra macros of muqarnas elements. Starting from a plan you can use the macros to build up a 3D model. Later Henk worked further on it. You can find his material at [url]https://www.fransvanschooten.nl/muqarnas.htm[/url]. If you're also interested in Islamitic Geometrical Patterns, then take a look at my GeoGebrabook on this related issue on [url]https://www.geogebra.org/m/kxp4qekc[/url].
Table of Contents
- domes
- Roman circular arcs
- from a circular arc to a dome
- domes and half domes in the Aya Sofia
- how to support a spherical dome?
- dome with cantilever construction
- dome with pendentives
- Cristo de la Luz (Toledo)
- dome 5
- arcs and domes
- dome 5 (2)
- dome 1
- dome 2
- dome 3
- dome 4
- dome 6
- dome 7
- dome 8
- dome 9
- layers and cells
- from tier to tier
- basic cel
- cells next to each other
- stacking cells
- intermediate pieces
- Basic shapes
- Biped and jug
- biped and almond
- stacking plaster cells
- examples
- 2 layers
- 4 layers
- Sultan Han - layers
- Sultan Han - from 2D to 3D
- Asjtarjan - layers
- Asjtarjan - square and rhombus
- Friday Mosque Isfahan southwest iwan
- Friday Mosque Isfahan southwest iwan back part
- Friday Mosque Isfahan northwest iwan - parts
- Friday Mosque Isfahan northeast iwan (2)
- Friday Mosque Isfahan souteast iwan
- Lahore Wazir Khan mosque
- Takht-i Sulayman
- La Zisa - Palermo
- La Zisa
- element A
- element B
- element C
- element D
- element E
- element F
- element G
- element H
- front view
- plan
- links
- links
Roman circular arcs
constructing circular arcs
In their constructions the Roman often used circular arcs. The great advantage of this type of construction is that only pressure occurs instead of pressure and traction. So stone can be used in its full strength, not as in architraves. With less material Roman could cross larger spans.
from tier to tier
A Practical Introduction to Muqarnas
On Youtube illustreert Eric Broug illustrates how to make a muqarnas model out of board paper. You discover how muqarnas are formed from tier to tier. On a frontal look you see a construction of cells. When you look on it from above you see a 2D tiling.
In following applet you can follow the construction of the capital of the film. In the graphic left you can see the top view zie je het bovenzicht. Right you can drag and rotate the 3D-view to look at the capital.
2 layers
Next construction comes from the website of [url=http://www.henkhietbrink.nl/]Henk Hietbrink[/url], in which he introduces muqarnas in workshops.
La Zisa
You can find rare examples of muqarnas outside of the Islam world in Palermo (Sicily). [br]A spledid exapmle is a niche in the central hall of the Castello della Zisa, the 12[sup]th[/sup] centure summer residence of the Norman kings.[br]Vincenza Garofaldo describes in detail this muqarnad and situates it with regard to the practices in the western and the eastern Islamic regions in the article [url=https://www.jstor.org/stable/25769702?seq=1]https://www.jstor.org/stable/25769702?seq=1]A methodology for studying Muqarnas: the extant Examples in Palermo[/url].
The muqarnas in la Zisa counts 12 tiers. [br]It's usual to use just a limited number of element types in a muqarnas. Often in one tier you can find just one element type. But in the muqarnas in la Zisa you can count not less than 8 different elements, combined in a complicated way and mixed over different tiers.[br][br]At first we'll take a look at these different types of elements, than we observe how they are combined in the muqarnas.
links
[list][*]On the website of the [url=http://www.sigd.org/resources/muqarnas/]School of Islamic Geometric Design[/url] you can find lots of materials on the construction of muqarnas and links to other sites.[/*][*]Eric Broug made a nice film on making muqarnas out of [url=https://www.youtube.com/watch?v=GH7N38vX-6I]cardboard[/url].[/*][/list]
[list][*]Thé database of muqarnas with many 2D schemes is the website of [url=http://www.shiro1000.jp/muqarnas/default.htm]Shiro Takahashi[/url].[/*][/list]
[list][*]Very nice is how [url=http://www.henkhietbrink.nl]Henk Hietbrink[/url] illustrates on his website how in workshops he works with a 3D printer, cut-out shapes and a STL viewer to show 3D animations in analysing many examples of muqarnas.[/*][/list]
Getty Publications put the book The Topkapi Scroll - Geometry and Ornament in Islamic Architecture of Gülrü Necipoglu online. You can legally download it at [url=https://www.getty.edu/publications/virtuallibrary/9780892363353.html]Getty Publications[/url]. Besides high quality reproductions of thé historical written source of islamic patterns and muqarnas, you get a standard work that situates the scroll into its historical-cultural-scientifical context.
Who's looking for supplementary mathematical-scientifical information surely will find what he's looking for in some publications, that you can find online as pdf-documents.[br][br][list][*]Don't the dissertation of Silvia Harmsen: [br][url=https://archiv.ub.uni-heidelberg.de/volltextserver/7047/]Algorithmic Computer Reconstructions of Stalactite Vaults - Muqarnas - in Islamic Architecture[/url].[br][/*][*]Very interesting too is the work of Yvonne Dold-Samplonius: [br][url=http://www.jphogendijk.nl/arabsci/Dold1.pdf]Practical Arabic Mathematics: Measuring the Muqarnas by al-Kashi[/url][/*][/list]