# Arabesque: Where Art Meets Mathematics

Associate Professor (Algebra)
Department of Mathematics and Statistics,
King Fahd University of Petroleum & Minerals (KFUPM)
Dhahran, Kingdom of Saudi Arabia
Co-Editor-in-Chief, Palestine Journal of Mathematics
Managing Editor, Arabian Journal of Mathematics

Saudi Aramco and produced
by Sultan Bin Abdel Aziz
Science & Technology Center

The main objective of this lesson is to illustrate an important application of mathematics in practical life -- namely in art. Most of the pictures selected for this lesson are visible on the walls of Al-Hambra – Granada (Spain), which is one of the most important landmarks in the Islamic civilization. There are three educational goals for this lesson: (1) establishing the concept of isometries; (2) giving real-life examples of groups; (3) demonstrating the importance of matrices and their applications. As background for this lesson, students just need some familiarity with the concept of a group and a limited knowledge about matrices and the inverse of a non-singular matrix.

Dr. Abuhlail is an Associate Professor in the Department of Mathematics and Statistics at King Fahd University of Petroleum and Minerals (KFUPM) in Dhahran, Saudi Arabia. He is from Palestine and his major area of study and teaching is Algebra. Dr. Abuhlail's interests include applications of mathematics in the real world, eLearning, the History of Mathematics, and Math Olympiads (regional and international). Dr. Abuhlail is also the Associate Managing Editor of AJS-Mathematics, a section of the Arabian Journal for Science and Engineering (AJSE).

This site has been recommended by Dr. Abuhlail as a source for more exercises like those provided in his lesson.
http://www.clowder.net/hop/17walppr/17walppr.html

This site, sponsored by the Oracle ThinkQuest Education Foundation, explains the basic mathematics underlying tessellations and also allows you to browse through many examples of tessellations in real life.
http://library.thinkquest.org/16661/

This resource, sponsored by the Math Forum@Drexel, presents an excellent overview of tessellations as well as numerous tutorials and lessons on that topic.
http://mathforum.org/sum95/suzanne/tess.intro.html

This site, presented by Illuminations: Resources for Teaching Math, provides a lesson in which students can explore regular and semi-regular tessellations.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L834