Tessellations lectures

The historic Islamic ornamental art in Iran (Emil Makovicky)

I shall start with the beautiful brick and plaster ornaments of the Seljuk era, show the first known quasiperiodic tiling and its subsequent development, and demonstrate the development of ornamental art in interaction with the development of glazing and colouring techniques in ornamental architecture. The principal approach will be thorough the symmetries of these creations but I’ll try to remain close to the knowledge level of the ornament creators and I promise not to suppress the aesthetic pleasure of the audience by dry theories.

Written medieval sources on Persian-Islamic tilings (Jan P. Hogendijk)

Decorative tilings were among the main achievements of medieval Persian-Islamic art. Therefore one mak ask the question what medieval Arabic and Persian manuscript sources tell us about the design of tilings. In this talk I will discuss three categories of such sources:

1. Scrolls, containing drawings without texts, such as the Topkapi Scroll.
2. Manuscripts containing drawings together with written instructions, such as an anonymous Persian manuscript in the National Library in Paris.
3. Works written by mathematicians such as the Introduction to Geometry by Abu’l-Wafa Buzjani (940-998), or a letter on algebra by Umar Khayyam (1048-1131). In such mathematical works, the design methods may be criticized or the relation to the tilings may not even be mentioned.

I will also discuss the way in which particpants of the summer school can access these medieval sources and/or their (extant and future) modern editions and translations in different languages.

slides.pdf, litterature.pdf

Experimentations in contemporary architecture (Jean-Marc Castera)

A presentation of my work as pattern designer in modern architecture with Foster+Partners architects. Work somehow inspired from a sentence of Houcine Lamane, a Moroccan Maallem (master of the art), saying he was “searching for the unknown flower, the flower coming from the future”.
When new experimentations contribute to enrich our knowledge of the tradition.

Traditional geometric art and quasicristals, an overview (Jean-Marc Castera)

Since the discovery of quasicrystals in 1982, there is a renewed scientific interest in traditional geometric art. Did the Persian and Moorish artists discovered the concept of quasicrystal, centuries before contemporary science? After an overview of the principles of the art we will review that controversial issue.

Symmetries in Persian traditional tilings (Meghdad Ghari)

Through centuries, Persian craftsmen have developed geometric designs, tilings and patterns with their own special characterizations distinguishing them from those used in other countries, particularly in the shape of tiles and motifs they consist of. In this talk, first we explain what we mean by Persian Traditional Tilings, and then we describe various traditional methods of their constructions. We also determine their corresponding symmetry groups. In this respect, we investigate well known tilings such as Darb-i Imam and Gunbad-i Kabud (in Maragha), as well as some other interesting tilings of Isfahan. Moreover, we show how geometric symmetries of such designs can be used in the classroom as a tool for teaching isometries of the plane to students.

What are Mathematics Houses? (Ali Rejali)

In this talk, the history, and the activities of the mathematics houses in Iran, as infra- structures for challenging mathematics outside the classroom, with emphasis on mathematics education and its effects on behavior of teachers and students, in their studies and their real lives, will be explained.
We also show that Mathematics Houses extend the possibility of popularizing sciences and Mathematical Awareness among School Students, University Students, Teachers, General Public and even the Blinds. We show that they are a place for developing the sustainable development of the country and enrichment of international relations for peace.

The application of geometric patterns and tilings in mathematics education (Akbar Zamani)

Mosaics and geometric patterns are helpful tools for improvement of mathematics talents and provide a challenging atmosphere in and outside the classroom. Drawing different geometric patterns by students encourages and attracts them to learn fundamental mathematical concepts. In this talk, I present some of the patterns used in Iran’s tilling and architecture, and its neighbors- such as Afghanistan, Pakistan, Iraq... Then, using these patterns, several mathematical problems are solved.

Workshop on tilings (Jean-Marc Castera, Emil Makovicky)