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Enduring Idea of the Unit: Ordered mathematical structures find expression in works of art.

Art Idea of the Unit: Particular mathematical concepts of order, such as transformations, pattern, and symmetry, may best be learned through experiences in art.

Key Questions

• Which shapes will tessellate, or tile a plane with no gaps or overlaps?
• Why will certain shapes tessellate and not others?
• Who was M.C. Escher and what does he have to do with tessellations?
• What is the connection between M.C. Escher and the Alhambra Palace?
• What cultural significance is behind the Islamic tile work at the Alhambra?
  

Unit Objectives

· Students will understand the relationship between
mathematical concepts by using tessellations and
symmetrical design patterns used in Islamic designs.( Art Production)

· Students will understand the concept of rotational,
reflectional, and translational symmetry. (Art
production)

· Students will understand the cultural significance of geometric pattern in Islamic design (Art history,
Aesthetics).

· Students will understand the philosophical and
mathematical connections between M.C. Escher's
symmetrical works and the tile designs of Islamic
craftsmen (Aesthetics).

Overview of Lessons

Lesson 1:
This lesson focuses on the historical and cultural background of the Islamic artists whose work influenced M.C. Escher in the 1930’s. Students are encouraged to make as many formal and philosophical connections as possible between M.C. Escher's symmetrical designs and the tile work he found during his visits to the Alhambra Palace.

Lesson 2: Radial Symmetry
The purpose of this lesson is to explore the mathematical concepts of transformation embedded in Islamic tile work and M.C. Escher's symmetrical drawings. In this lesson, students will compare and contrast the different aspects of transformation geometry and define reflective, rotational, and translational symmetry. Activities encourage exploration of geometric shapes in order to apply these concepts.

Lesson 3: Congruent Shapes and Tessellations
The purpose of this lesson is for students to design a tile shape using the mathematical concepts from the previous lesson and then use that design to create an original tessellated pattern in the tradition of Moresque design.

Resources and Materials

Books and Publications

Critchlow, Keith. Islamic Patterns: An Analytical and Cosmological Approach. New York: Shocken Books, 1976.

Escher, M.C. Escher on Escher: Exploring the Infinite. New York: Harry N. Abrams, Inc., 1989.

Escher, M.C. M.C. Escher: The Graphic Work. New York: Barnes and Noble Books, 1994.

Grabar, O. (1992). The Mediation of Ornament. New Jersey: Princeton University Press.

Wilson, Eva. Islamic Designs for Artists and Craftspeople. New York: Dover Publications, Inc, 1988.

The North Texas Institute for Educators on the Visual Arts and this newsletter are supported by grants from the Edward and Betty Marcus Foundation; the Greater Denton Arts Council and the Arts Guild of Denton; the Texas Commission on the Arts; and Individual Donors. The Institute collaborates with school districts, museums, and art organizations within the state of Texas. The NTIEVA Newsletter is published by the North Texas

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