www.fransvanschooten.nl

My favorite

One of my favorite mosques in Istanbul is the Yavuz Selim Mosque.

From the center, I walk via the Şehzade and Fatih to Yavuz Selim, high on a hill. I love the serene tranquility of this mosque with its beautiful garden. At the feet of the terrace lies the old city and across the Golden Horn there are the skycrapers of Taksim and Levent, but in the garden, I am out of reach of the city noise of screeching sirens, motorbikes, and honking cars.

ArchNet: Sehzade

ArchNet: Fatih

ArchNet: Yavuz Selim

 

3D printing

The teaching material consists of six boxes for six groups of three to five students, each with nearly 200 muqarnas pieces of two by two centimeters and four centimeters high. Everything is printed on a Flashforge Adventurer 3 using PLA from Kexcelled. This PLA can be processed better on the Flashforge than other popular brands. Printer and PLA supplier is Badgers Lair based in Hoevelaken. They also did the consultancy and printed large demonstration objects.

BadgersLair.nl

 

Chris Cambré

The Belgium master of Geogebra created a workbook with animations and pictures to explain the basic ideas of muqarnas. Chris Cambré has travelled through many countries and created geogebra workbooks on islamic geometry.

Muqarnas

Islamic Geometric Patterns

 

Ali Reza Sarvdalir

Muqarnas

In Islamic mosques you often see abstract decorations in an interplay of regularity and variation. Muqarnas are decorative elements that, for example, fill the space above the entrance to a portal. It looks like a large niche being filled with all kinds of small niches. For the craftsman, it is a technical challenge to design new creations within the available space with a limited number of standardized building blocks or units. You can find beautiful examples in Turkey and Iran, but also in Moorish Spain or Morocco. The formal language is a fine application of mathematics and lends itself well to an alternative class lesson.

We investigated many muqarnas.

Geogebra book with animations and tutorials

Prof. Dr. Uluengin

Starter work pieces

Natanz

Student work pieces

Kayseri

Bursa Abdal Mehmet Camii

Çorum

Nigde Ak Medresse

Amasya

 

Golpayegan

 

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Puzzle

On the left, you can see a 3D drawing of a reconstruction of a famous muqarnas that does not exist anymore. On the right there are two alternative interpretations which are really different from each other. Try to find out the difference.

 

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Takht i Sulayman Southern Vault
© M. Yaghan

Design Yaghan

Alternative Design

The design in the middle matches the drawing at the left, but the right one is a full layer higher. Printing designs in 3D helps to investigate the true mature of these muqarnas.

 

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Workshops

During workshops, students discover how to investigate patterns. It is all about how to build a complex architecture with a limited set of basic figures. Student can start with design drawings in the flat plane by placing pieces of paper next to each other like a puzzle. Next, they can create the design drawing with 3D printed units. During the workshop, we bring in the 3D printed units. As an alternative, we created an online environment to develop muqarnas in GeoGebra.

Geogebra book with animations and tutorials

 

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Karbandi and muqarnas

Muqarnas are decorative elements. Karbandi are constructive elements. Karbandi are the arches that carry a dome. The pressure of the building mass of the round dome is directed through the karbandi to the walls of the underlying rectangular box.

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Sources

Earlier workshops on muqarnas have been held by Bart Post, Maartje Elsinga-van der Veen, Susanne Tak, Rogier Bos, and Philip van Egmond, among others. They teach the system "back on front", neglecting the system "back on curve". Common sources are the dissertation by Sylvia Harmsen and articles by Yvonne Dold-Samplonius. Her thesis covers both systems.

Dissertatation: Algorithmic Computer Reconstructions of Stalactite Vaults - Muqarnas - in Islamic Architecture, Harmsen, Silvia

The Topkapi Scroll: Geometry and Ornament in Islamic Architecture Gülru Necipoğlu (PDF)

Thesis: Geometry of Muqarnas in Islamic Architecture, Sakkal, Mamoun (PDF)

 

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Examples of the twelve basic units

With a limited number of standardized building units, all different kinds of muqarnas can be built. Below are examples of the twelve basic building units for the 45° system based on squares, parallelograms and triangles whose angles are multiples of 22.5° are, for example, 45°, 67.5°, 90°, 135°. The top row shows the units with walls, the bottom row shows the intermediate units. An other system is based on 30° angles.

Shapes can be defined by their angles. Every shape is symmetrical. Its symmetry line is a diagonal of a quadrilateral or a perpendicular bisector of a triangle. We code units by counting the quarters of a right angle, starting at the point of the unit, along the diagonal, to the wall and round to the point. Square A is therefore 2-2-4 because its angles are 45°, 45°, and 90°. Rhombus B is therefore 3-3-2 and large biped J is 5-2-1.
 

 

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Coding

For in-depth analysis of the structure of muqarnas, I develop software that generates drawings, tables and statistics for any muqarnas. Input is a series of coded strings. The software interprets these strings using the geometrical definitions of a collection of muqarnas units. For the software, a muqarnas is a collection of strings of letters, where each letter represents a unit. The letters A to F have been chosen for the top row of units with rear wall and the letters G to L for the bottom row of intermediate units without rear wall. One of the aims is to identify for each unit its neighbours (left, right, above, and below) and to detect missing neighbours and other inconsistencies.
During my inquiries, I found out that I needed more, dedicated units for special purposes, for example at the end of a layer or in the middle of a layer to gain extra height. These new units are often half the size of a standard unit, but can also be something surprisingly new. These units are also coded. For example, the codes A1 and A2 represent the left and right half of the blue square building block that got the letter A. An example of a new building block is the flat wall, coded with the letter Z. The software accepts all triangular and quadrangular shapes.

A kind of inversion of the pink almond, being the full unit, and the small biped, being the intermediate unit, does exist: a pink small biped, being the full unit, and an almond, being the intermediate unit. This new unit has nice properties. See the alternatives at the inquiry of Çorum.

Inquiry: Çorum

For students, assignments have been made with increasing complexity, depending on the level of the student and the available lesson time. The easy starter assignment has only two layers and is coded as:

D L C C L D
A J A I E I A J A

 
Easy starter assignment

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The student basic assignment is coded this way:

C C C C
F I D I D I D I F
J C C C J C C C J C C C J C C C J
I E I A I I A I E I I E I A I I A I E I

 
Student basic assignment

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GeoGebra Books

Visualizations have been made in a seperate GeoGebra book, including workshop materials.

Visualizations

Workshop materials

 

3D printed units

Six boxes with 3D printed muqarnas units are made available. Each box contains about ten to twenty pieces of each of the twelve basis units. Additional pieces with special characteristics are available too.

 

 

Detailed information

More detailed information about the basic asignment, including pictures and samples of 3D models, is available at a seperate webpage.
Details of Student Basic Assignment
Details of Easy Starter Activity

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Student Basic Assignment

At the NVvW 2019 study day, three helpful children asked if I may need their help. I was curious how far they would come with a minimal explanation. Within half an hour, they assembled their muqarnas from 3D printed units.

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all the details and a full screen animation

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Easy Starter Activity

Young students start with an easy assignment where the rules are quickly discovered. This two-layer muqarnas follows the rule "back on front". Students were handed over a construction plate for a quick start.

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all the details and a full screen animation

 

 

 

Detailed information

More detailed information on Mr Uluengin and his book is available at a seperate webpage.
Detailed inquiry: Prof. Dr. Uluengin

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M. Fatin Uluengin

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all the details and a full screen animation

 

 

Bursa

Bursa is the fourth most populous city in Turkey with large industries. In the fourteenth century, it was the capital of the Ottoman State. Bursa has a modern Science Center. Every year, they organize the Turkish Airlines Science Expo, a four day experience with more than hundredthousand visitors. Mountain Uldağ is a lovely place, in winter there are ski resort, in summer it hosts the Bursa AstroFest.

Wikipedia: Bursa

Bursa Science Expo

Uludag Astrofest

 

Detailed information

More detailed information on this Bursa muqarnas, including pictures and samples of 3D printed models, is available at a seperate webpage.
Detailed inquiry: Bursa Abdal Mehmet Camii

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Bursa Abdal Mehmet Camii

In Bursa, you will find the Abdal Mehmet mosque. This muqarnas follows the rule "back on curve".

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all the details and a full screen animation

 

ArchNet

Description from ArchNet: The mosque that bears the name of celebrated mystic Abdal Mehmed in Bursa was founded by Basši Ibrahim, a rich merchant of Bursa who also built the Basši Ibrahim Complex.

ArchNet

 

Nigde

Nigde is a small city with some tourist attractions including an archeology museum and the Alaaddin mosque with its beautiful muqarnas.

Wikipedia: Nigde

Wikipedia: Nigde Alaaddin Mosque

 

Detailed information

More detailed information about the Nigde muqarnas, including pictures and samples of 3D printed models, is available at a seperate webpage.
Student activity: Nigde Ak Medresse

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Nigde Ak Medresse

The mosque Ak Medresse is situated in Nigde. The Turkish architect M. Fatin Uluengin has written a valuable book about muqarnas.

My reconstruction may have been done according to the rules, namely "back on front", the result looks weird and does not match the photo. The first layer is much too wide. Moreover, the photo shows five layers and the reconstruction only four layers. After implementing the additional rule "back on curve", the missing layer becomes visible. Instead of the blue "intermediate units" there will be muqarnas units with a wall. The result is a slimmer and higher muqarnas that matches both Uluengin's analysis and the photo.
Below, the five-layer reconstruction is shown which is based on the rule "back on curve".

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all the details and a full screen animation

 

ArchNet

Description from ArchNet: Ak Madrasa, whose architect is unknown, was commissioned by Ali Bey under Karamanid rule in south-central Anatolia. It is a double storey building with a flat roof, centered on an open courtyard, and with a symmetrical plan aligned north south, measuring approximately twenty-two meters by twenty-five meters.
The entrance, which is reached by descending twelve steps form the street level, is through the muqarnas pishtaq on the north fašade. The building's name, which means White Madrasa, refers to this white marble pishtaq. A vaulted passageway leads into the courtyard through the portico. The courtyard has a well at its center and measures about eight and a half by nine and a half meters. It is framed by the main iwan on the south and wrapped by a double-story portico on the other three sides.

ArchNet

 

Natanz

Natanz is a small city with a long history. Its monuments deserve a visit.

Wikipedia: Natanz

 

Detailed information

More detailed information about the Natanz muqarnas, including pictures and samples, is available at a seperate webpage.
Detailed inquiry of Natanz

 

 

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Natanz

Natanz is a city between Teheran, Kashan and Isfahan with a beautiful great mosque. Yaghan and Harmsen described an example of a muqarnas in a niche, which is situated in the basement vault of the north iwan in that mosque (Masjid-i Jami).

Blair has written in detail about the shrine complex of Natanz.

Harmsen investigated a muqarnas in a niche into great extent. She made a replica of carton. Interesting is what happens at the third layer. She did fill in the gap in the paper version, but not in her computer models. Her rules to generate and interpretet graphs do not help her to solve what she omits: sometimes, you need flat walls. As a result, the software does not understand how to connect tiers, especially the rhombus at the first and second layer. In my interpretation, I added flat walls and a new non-standard muqarnas unit: a half square with a wall at the short side (instead of its wall on the long side.

Yaghan also studied this muqarnas. His drawings are very precise, but do not tell which object is drawn. In my analysis, I labeled every unit. Four units could not be recognized. My assumption is a combination of flat walls and a non-standardhalf square. Questions arise about the need of drawing the the short diagonals of the rhombus and the meaning of the large rectangle. His analysis drawing is almost identical to Harmsen, but there are differences, small in detail, but major impact on the interpretation. That is why I developed the paper 2D analysis, bought a 3D printer, started printing 3D objects and developed dedicated software to find out whether these differences matter.

Blair, S., The Ilkhanid Shrine Complex at Natanz, Iran, Cambridge Harvard University Press, 1987
Blair, S., Bloom, J.M, The Art And Architecture Of Islam (1250- 1800), New York, Yale University Press, 1994
Harmsen, S., Algorithmic Computer Reconstructions of Stalactite Vaults - Muqarnas - in Islamic Architecture, 2006, PhD thesis
Yaghan, M., Decoding the Two-Dimensional Pattern Found at Takht-i Sulayman into Three-Dimensional Muqarnas Forms, Iran, Vol. 38 (2000), pp. 77-95

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all the details and a full screen animation

 

ArchNet

Description from ArchNet: The Great Mosque of Natanz is located on a site occupied since the Buyid period (tenth century). In the fourteenth century it took the form it does today. Today the mosque complex contains a four-iwan mosque, an octagonal sanctuary, a minaret, and a mosque from the 1930s fronted by a fourteenth-century khanqah portal.

ArchNet

 

Kayseri

Kayseri is a city with sturdy Byzantine city walls and Ottoman mosques decorated with attractive muqarnas.

Wikipedia: Kayseri

 

Detailed information

More detailed information about the Kayseri muqarnas, including pictures and examples, is available at a seperate webpage.
Detailed inquiry of Kayseri

 

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Kayseri Cifte Madrasah Gevher Nesibe

Above a door of the Cifte Madrasah Gevher Nesibe hospital, a muqarnas with a special set of two non-standard building units has been realized. The set creates space within the square surface of the underlying layer for a smaller building unit on the next layer. As a result, the surface of a standard square is doubled in height.

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all the details and a full screen animation

 


Harmsen and Krömker describe this extraordinary unit because their software did not recognize its geometry.

Researchgate: Seljuk Muqarnas along the Silk Road

Shiro Takahashi: muqarnas database

ArchNet

Description from ArchNet: The Çifte Madrasa is so named because it consists of two adjacent four-iwan buildings oriented north-south. The one to the east was founded as a medical school by Sultan Giyaseddin Keyh&uul;srev (1192-1197 and 1205-1211) and the other was founded as a hospital by his sister Gevher Nesibe Sultan. The complex is not only the first Seljuk madrasa in Kayseri, but also the oldest hospital in Anatolia.

ArchNet

 

Çorum - Osmancık

In the Turkish district Çorum you will find the city of Osmancık.

Wikipedia: Çorum

Wikipedia: Osmancık

 

Detailed information

More detailed information about the Çorum - Osmancık muqarnas, including pictures, 3D models and examples, is available at a seperate webpage.
Detailed inquiry of Çorum

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Çorum

In the province of Çorum in the city of Osmancık there is a mosque with an interesting muqarnas. This muqarnas follows the line "back on front". The muqarnas can be built from the standard basic units, with a few exceptions. Half of a standard intermediate unit is required on the first building layer. In the second, half of a unit is needed. In the third building layer half of a standard intermediate unit is also needed.

Shiro Takahashi's drawing suggests some unique units in the top layer. This muqarnas needs further study at this point. The assignment for students is slightly different and solely based on standard building units.

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all the details and a full screen animation

 

Amasya

Amasya is an ancient city with a long history that starts before the Roman times. It was also an important city in Ottoman times. Sultan Selim I was born there, for example.

Wikipedia: Amasya

Archnet: Amasya Bimarhanesi

 

Detailed information

More detailed information about the Amasya muqarnas, including pictures and 3D printed models, is available at a seperate webpage.
Detailed inquiry of Amasya

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Amasya / Bimarhane

The Bimarhane mosque is located in Amasya. In the entrance portal, two small muqarnas are incorporated in the wall on the left and right. This muqarnas follows the line " back on front " and has as exception only two half intermediate units. That is why the assembly of this muqarnas is a clear assignment for young students.

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all the details and a full screen animation

 

ArchNet

Description from ArchNet: The Bimarhane of Amasya is dated to the year 1308. Today the Amasya Bimarhane is a museum dedicated to the history of medicine and surgery named after Sereffudin Sabuncuoglu who was a surgeon and physician active in Amasya during the Ottoman period. The building is entered through an ornate portal on its west side. This portal consists of an arched doorway within a shallow iwan surmounted by a muqarnas hood and framed with bands of vegetal and geometric ornament carved in stone. Within the recessed entryway are two smaller muqarnas niches surmounted by inscription bands.

ArchNet

 

Detailed information

More detailed information about the Golpayegan muqarnas is available at a seperate webpage.
Detailed inquiry of Golpayegan

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Golpayegan

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all the details and a full screen animation

 

ArchNet

Description from ArchNet: The Friday Mosque of Gulpayigan was built by Seljuk Sultan Muhammad Tapar I (1105-1118), son of Malik Shah I. Only the dome chamber remains from the Seljuk period mosque, which was integrated into a monumental four-iwan mosque during the Qajar period. The square dome chamber, or sanctuary, is constructed entirely of brick and is opened on three sides with vaulted archways flanked by embedded columns. The east and north corners of the chamber have thick double columns marking the corner, flanked by narrow archways cut into the adjoining walls that are topped by arched windows. Only a single such archway exists at the western corner and there are none at the southern corner. Above, the transition to the shallow brick dome is achieved with muqarnas squinches built into the corners of the tall octagonal drum. Light comes in through four honeycomb windows pierced into the dome's base, which is ringed with a band of Kufic inscriptions.

ArchNet

 

 

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Chris Cambré: Muqarnas

Yaghan: An online course to Muqarnas

Harmsen, Kröker: Seljuk Muqarnas along the Silk Road

Eric Broug: A Practical Introduction to Muqarnas

Abdelghani Nhari: Constructing a Muqarnas Composition

Eric Broug: Muqarnas

Dan Owen: Muqarnas

Shiro Takahashi: muqarnas database

Cristˇbal Vila: Isfahan

Dan Owen: interactive course

Yaghan: Decoding ... Takht-I Sulayman

Beyşehir: Eşrefoğlu

Video Beyşehir: Eşrefoğlu

Presentatie Vaknetwerk Amsterdam

Presentatie Studiedag NVvW

The Topkapi Scroll: Geometry and Ornament in Islamic Architecture Gülru Necipoğlu (PDF)

NRC Handelsblad: Een zevenhoek te Isfahan

Practical Geometry: Muqarnas

Hogendijk: Sources relating to Arabic-Islamic science

Nieuw Archief voor Wiskunde: De Sleutel tot de Rekenkunde van al-Kashi

U Talent: Islamic Patterns and Muqarnas

Publication in Euclides: Creatief 'DrieDee': Muqarnas

NWD 2016: Powerpoint and handout

 

 

 

 

 

 

 

 

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