In this activity we approach an art form that is internationally known as “tessellation”. This art form becomes the occasion and the context in which, participants, will approach interdisciplinary concepts related to regular polygons. Participants are asked to observe works of art with repetitive patterns, identify the basic repetitive “mosaic” and create their own representations. At the same time, through a series of images with floors, mosaics and carpets with repeating patterns from Roman, Arabic, Persian, Byzantine and contemporary art, the participants seek to recognize geometric shapes in various art forms.

Objectives:

To get acquainted with the repetitive designs (patterns) in different periods and art forms.
To recognize through art geometric shapes and patterns.
Look for and identify various repetitive patterns in their immediate environment.
To recall and deepen the concepts of axial and central symmetry
Understand the concept of tessellation and its interconnections with geometric transformations
Strengthen their cultural capital by broadening their perspective on mathematics and their relationship to art.

Duration: 90 min

Number of participants: 10 – 15

Materials:

Computers, internet connection

Description:

Exercise flow:

Phase 1: Repetitive patterns in works of art

Phase 2: Repeating patterns and repetitive tessellations

Phase 3: Repeated tessellations around us, our own tessellations

In the first phase of the activity the instructor asks the participants to visit the page:

http://www.greatbuildings.com/cgi-bin/gbi.cgi/The_Alhambra.html/cid_2343497.gbi

After noticing various works of art with repetitive shapes, complete the table below:

Art object (painting, paving, mosaic, etc.)

Repeating Geometric Shapes

The aim of the first work is for the participants to recognize geometric shapes, with emphasis on regular polygons, in various art forms and to recall related geometric terms. The geometric shapes that will be found in the works of art can be repeated either randomly, as is the case in Klimt’s works, or based on a specific pattern, as in the vessels of the geometric period, or create repetitive tessellations, as in the case of Arabic art.

In the second phase we ask the participants to tell us which of the following works of art have simply repetitive shapes and which can be considered tessellations.

The term tessellation refers to any repetitive pattern of interlocking shapes in such a way that a surface is covered without gaps or overlaps.

The second phase of our activity aims to focus on projects that can be considered tessellations through examples and counter-examples. We show the participants the photos and give them the short definition of tessellations. The rapporteur can enrich this report by giving participants additional information.

Figure 1: This is the painting entitled “Reptiles” by the Dutch painter M. Escher. The pun on its English title “Rep-tiles” is well known, which is considered an abbreviation of the term repeat tiles. This table can be considered tessellation, with the reptile being repeated in a basic way that does not leave gaps or create overlaps.

Figure 2: This is a close-up photo of a honeycomb. It is clearly a tessellation, with the regular hexagon as the basic mosaic; a work of art made by nature!

Figure 3: In the photo with the dry mud we have no tessellation, there is no normally repeating shape, as each tile has a different shape.

Figure 4: This is the painting entitled “Various Circles” by Kandisky. The repetition of circles in different sizes is done in a random way, the circles overlap, while there are huge gaps between them. Clearly, then, it cannot be considered a tessellation.

Figure 5: This is a representation of a part of a Byzantine floor, consisting of isosceles triangles – a classic case of tessellation.

Figure 6: This is the painting entitled “Great Composition of Hydra” by N. Hatzikyriakos-Gikas. Here the painter is influenced by the principles of cubism. The surface is covered by geometric shapes, but the work can not be considered tessellation, as there is no basic repeating mosaic.

We close the second phase of the activity with the question: Which of the tessellations did you like the most and why;

………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

This question is open and aims to involve the personal element. The participants will express their opinion and will argue about it. This can be an occasion for indirect repetition of geometric terms and properties of geometric shapes.

In the third phase of our activity we ask the participants if they can think of some tessellations that they encounter every day in nature, at home or at work.

Participants should apply their knowledge and look for tessellations in their immediate environment. Chess, the brick walls of a building, the turtle shell, the pine cone, the carpet, the grandmother’s embroidery are just some of the recurring resolutions they may mention.

Finally we ask them to draw their own tessellation?

In this exercise the participants are more experientially involved and create their own tessellation. This exercise can take place in the last hour of the activity, as long as the rapporteur has made sure that there is a time proximity to the execution of the other parts of the activity.

Expected outcomes:

At the end of the activity participants will be able to:

They discover the regularities inherent in a work of art, through the recognition of the geometric transformations that take place in it.
They create their own tessellation

Sources

Field, R., Geometric Patterns: From Islamic Art and Architecture, Tarquin, 1998.

Gerdes, P., Geometry from Africa: Mathematical and Educational Exploration: The Mathematical Association of America, 1999.

http://www.greatbuildings.com/cgi-bin/gbi.cgi/The_Alhambra.html/cid_2343497.gbi