Springer Online Catalogue

Video and Multimedia at the 3ecm

  Costa, A.F., U.N.E.D., Madrid, Spain; Gomez, B., U.N.E.D., Madrid, Spain; Mora, J.

Arabesques and Geometry

1999. VHS/NTSC video tape. 3-540-92639-9

The authors of this film explain the topic of symmetry in mathematics with examples from Islamic art. The mathematical background - plane crystallographic groups - is spectacularly illustrated by examples at the Alhambra in Granada, Spain. This film will be enjoyed by everyone interested in mathematics, from school students to researchers. (Springer Verlag)

"The primary purpose of this video is to explore algebraic group structures that arise when describing certain patterns. The patterns discussed arise naturally in Arab culture and are expressed in the art form known as the arabesque.

The setting of the video is the Alhambra, in Spain (a natural choice for two Spanish authors), in which almost all types of arabesques can be found. The scenes are very picturesque and provide a concrete image to associate with the mathematics being discussed. The narrator has a very soothing (almost meditative, but not monotone) voice and moves at a reasonable pace. There are really two main parts to this video, dictated by the difficulty of the content.

The first ten minutes (of twenty) are devoted to a quick, yet thorough, discussion of rigid transformations in the plane (e.g., rotation, reflection, and translation). This portion is a truly excellent motivational lesson which can be especially useful in a geometry course designed for elementary education majors.

The examples and animation sequences beautifully illustrate the mathematics and would be appreciated by undergraduates.

The second half, however, is a bit more advanced. It focuses primarily on the classification of the 17 plane crystallographic groups and the connection to arabesques. This portion of the presentation is perhaps more suitable for a student of abstract algebra..." (Mark McKibben for MAA Online book review )

Mark McKibben (mmckibben@goucher.edu) is assistant professor of mathematics at Goucher College in Baltimore, Maryland. His research areas are nonlinear analysis, abstract evolution equations, and integral equations. He is the co-author of the book Algebra (with Dave Keck and Shane Rosanbalm, 1998, 2nd edition) and is currently co-authoring the texts "Real Analysis" and "An Introduction to Higher Mathematics."

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