This is an enjoyable, participatory activity in which attendees will get to work with the digitally manufactured pieces recreating different Moorish architectural elements features that can be seen in the exhibition “Al-Andalus Mathematics Tour,” as a strategy to make it easier to understand them. For this purpose, the pieces will be modeled with software and either printed with a 3D printer or cut out using a laser cutting machine.

Those attending will get the chance to work with a section of Muqarna ceiling work, the ribbed domes in the Cordoba Mosque, mosaics which cover the walls of the Alhambra and Real Alcázar in Seville, as well as the family of mosaics produced with tiles known as Girih.

The workshops were designed for people with or without specific training but with interest in Science and/or Art, students from the first year of secondary school, the first and second year of the baccalaureate, university students majoring in Teaching, Art History, Computer Science, Mathematics or Architecture.

They will be taught by Sergio Alonso Burgos, a professor of Computer Languages and systems at the University of Granada, and Álvaro Martínez Sevilla, a researcher at the Inter-university Research Institute Data Science and Computational Intelligence (ASCII), and the scientific director of the outreach and scientific tourism project “Al-Andalus Mathematics Tour” with the Descubre Foundation.

Spaces are limited. In order to participate, you must register in advance using one of the following forms: WORKSHOP 1(10:30 a.m.) | WORKSHOP 2 (11:45 a.m.)

ABOUT THE MATERIALS
Muqarna ceilings
These are one of the typical forms of decoration in Islamic art. These ceilings are composed of a series of seemingly whimsical shapes, with numerous peduncles hanging down to form complex dome-like structures. These ceilings, despite their apparent complexity, are made up of a small number of different pieces that can be combined together to create different patterns. Each piece is made using a simple prism to which a series of straight or circular cuts have been made. At the workshop, we will show a reproduction of several of these pieces which, by means of a series of magnets, will allow us to assemble the central section of a “muqarna” ceiling. We can see the central part of the Puerta del Lagarto, in the Giralda of Seville, and the Corral del Carbón in Granada.

Cross-ribbed domes
These are one of the most significant innovations in Cordoba’s Caliphate architecture. Three systems were developed, which we will reproduce in the workshop, and which vary in the manners of crossing their ribs, with 8 arches and 4, 8 or 12 crosses in accordance with specific geometric principles. We will be analyzing the three existing types and examine the keys to one’s success throughout history. We also have available -in laser-cut MDF wood- the most complex cross-ribbed dome in the world, with 12 arches and 16 crosses, that of the Great Almoravid Mosque of Tremecén.

Mosaics
One of the most common artistic manifestations in Al-Andalus art are the mosaics that cover walls, ceilings and floors. These mosaics are usually made up of relatively simple pieces used to fill a flat surface by means of translations, rotations and symmetries. At the workshop, we will be using reproductions in DM wood, painted in two colors, of several of the best-known mosaics found in the Alhambra and Seville’s Real Alcazar. These reproductions can be handled as if they were puzzles in which the participant must understand the rules used to put each of the pieces in place, so as to cover the surface.

Tiles known as Girih
These are a set of 5 geometric tiles (regular decagon, elongated hexagon, bow tie, rhombus and regular pentagon) that make it possible to cover the surface in various ways. They have recently been discovered as a result of a scroll found in the Topkapi Palace. Their use has been intense in Islamic art because they make it possible in a very simple way, to create complex interlacing patterns (interlaced bands). At the workshop, we will be using reproductions of these tiles with which the participants will be able to create their own latticework motif, or try to imitate one of those already existing.

In the multi-player dynamic geometry environment produced using NeoTrie VR Virtual Reality, participants will be get the chance to assemble different muqarnas and ribbed dome roofs virtually. They will also be able to build step-by-step simple geometric models of towers, arches and other architectural features, with the help of tools available in the software.

The workshops are designed for people with or without specific training who have an interest in Science and/or Art, students from the fourth year of secondary school, the first and second year of the baccalaureate, and university students majoring in Teaching, Art History, Mathematics or Architecture.

They will be taking place on Saturday, May 11 at 10:00 a.m. and 11:45 a.m. In order to participate, you must must register in advance by filling out this form: Workshop 1 (from 10:30 to 11:30 a.m.) | Workshop 2 (11:45 a.m. to 12:45 p.m.).

The organization will provide participants with Meta Quest 2 devices and a tablet for each device, so that they can take part in the activity.

It will be given by José Luis Rodríguez Blancas, a professor of Geometry and Topology at the University of Almería, where he teaches various subjects in the degree of Mathematics and in the Master’s degree of Secondary Education. He is currently a member of the group of Innovation and Research in Science and Mathematics Education at the University of Almeria. He led a UAL-FEDER Project (2021-23), using Neotrie VR at several primary and secondary schools, and he has taken part in the project Erasmus + KA2 Geometrician’s views (2021-23). He is a member of the team for the project Mathematics Tours.

SCENARIOS
Muqarna ceiling vault
Participants create virtual copies of different muqarnas and put them in place appropriately in order to form a three-dimensional vault. Then they create different prisms, known as Conza, Half Square, Dumbaque and Jaira, from which the adarajas are obtained, making concave cuts appropriately.

Ribbed vaults
Symmetrical models of 3 ribbed domes in the mosque of Cordoba are built here (Chapel of Villaviciosa, Maqsura and side of the Maqsura, which are formed by 8 arches, with 4, 8 and 12 crosses, respectively).

Torre del Oro
The participants build a simple dodecagonal prism model of the Torre del Oro of Seville step by step, reproducing a hexagonal prism. They add round bodies (spheres, cylinders and cones), and animate a spiral staircase inside of it using dynamic geometry tools available in the software.