www.fransvanschooten.nl

Work in progress

This webpage is in development. A lot of research has to be done. My aim is to develop rules for drawing and analysing muqarnas. Visualisation is a major issue. The actual coloring scheme is just a try out and needs improvement.

3D printing

The teaching material consists of six boxes for six groups of three tot 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

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 elements. 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.

 

4

4

4

Takht i Sulayman

2D design

3D print

Student work pieces

Student activity: Bursa Abdal Mehmet Camii

Student activity: Nigde Ak Medresse

Inquiry: Natanz

 

During the workshop, you may discover how to teach your students to work with patterns. It is about how to build complex architecture with a limited set of basic figures. They 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 elements. In the Turkish city of Beyşehir is the Eşrefoğlu mosque, built in the thirteenth century, with beautiful muqarnas. Eric Broug has posted inspiring videos on YouTube. During the workshop, we bring in the 3D printed elements with us.

Eric Broug: A Practical Introduction to Muqarnas

Abdelghani Nhari: Constructing a Muqarnas Composition

Eric Broug: Muqarnas

Dan Owen: Muqarnas

Cristóbal Vila: Isfahan

Dan Owen: interactive course

Yaghan: Decoding ... Takht-I Sulayman

Beyşehir: Eşrefoğlu

Video Beyşehir: Eşrefoğlu

Presentatie Vaknetwerk Amsterdam

Presentatie Studiedag NVvW

 

top
 


Karbandi

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.


Drawing in SketchUp


Result in 3D

2

2

 

top
 


Sources

Earlier workshops on muqarnas have been provided by Bart Post, Maartje Elsinga-van der Veen, Susanne Tak, Rogier Bos, and Philip van Egmond, among others. Common sources are the dissertation by Sylvia Harmsen and articles by Yvonne Dold-Samplonius.

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

NRC Handelsblad: Een zevenhoek te Isfahan

Concrete Meetkunde: Muqarnas

Hogendijk: Sources relating to Arabic-Islamic science

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

U Talent: Islamitische patronen en Muqarnas

Artikel Euclides: Creatief 'DrieDee': Muqarnas

NWD 2016: Powerpoint en handout

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

 

top
 


2

top
 


Student work pieces

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. They quickly realized the system of papers with red arrows and green lines and they quickly discovered which 3D piece belonged to which paper. Within half an hour I received the photos below.
Math teachers, on the other hand, work much more thoughtfully, go for complete understanding, and needed more time.


Design in 2D


Result in 3D

2

2


Teachers in action

2

 

 

 

 

 

 

top
 


Bursa Abdal Mehmet Camii

In Bursa, you will find the Abdal Mehmet mosque. The artist Shiro Takahashi has created a database with drawings and photos of muqarnas.


Bursa


Analysis drawing Shiro Takahashi

2

2


Matching


Student activity

2

2

 

 

 

 

top
 


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 tier is much too wide. Moreover, the photo shows five tiers and the reconstruction only four tiers. Implementing the additional rule "back on curve", the missing layer becomes visible. Instead of the blue "intermediate elements" 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-tier reconstruction is shown which is based on the rule "back on curve".


Nigde


Muqarnas

2

2


Analysis by M. Fatin Uluengin


Student activity

2

2


Construction plate


Model

2


Computer reconstruction (STL) inside bottom view


Computer reconstruction (STL) inside left view

2

2

 
The first attempt was based on the rule "back on front". It contains four tiers.


Computer reconstruction (STL) inside


Computer reconstruction (STL) outside


Model

3

3

3

 

 

 

 

 

 

 

top
 


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).


Natanz

 

2


Muqarnas
© Margi Rothengatter-Lake


Muqarnas

2

2


Mosque


Student activity

2

2


Computer reconstruction STL


Computer reconstruction STL

2

2


Construction plate


Model

2

2

 

 

 

top
 


https://www.todocoleccion.net/libros-segunda-mano/primera-sigunda-parte-reglas-carpinteria-por-d-lopez-arenas-1619-facsimil-1966~x42835811 http://www.alhambra-patronato.es/mocarabes-versus-muqarnas-2
 Dutch