Touching Soap Films
and
Arabesques and Geometry
Reviewed by Mark McKibben
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Touching Soap Films
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This video is a computer-generated adventure into the world of minimal surfaces. Historically, the beginning of this field of study dates back to at least 1760 when Lagrange posed the question, "Does there exist, for each arbitrarily complicated boundary curve, a surface of least area (i.e., a minimal surface)?" The purpose of this 40-minute featurette is to expose its audience to both the historical development and modern research in the field. It does certainly leave an impact on the viewer, but this may not be entirely due to the exposition of mathematics.
Let me describe the setting of this video. The underlying story is an adventure through a museum (of sorts) of surfaces. A boy by the name of Kalle is intrigued by the plethora of surfaces he encounters along his journey to this building and decides to investigate further. He proceeds inside the building and after a rather bothersome run-in with a computer sentinel standing guard of the building (as though it were a military fort of some kind), he stumbles into the shrine of the grand-daddy of all surfaces. Needless to say his curiosity gets the best of him and he manages to demolish it with one foul swoop. He is immediately escorted to the professor's office where his lesson on the history of minimal surfaces begins (of course, after being chastised for his utter carelessness). The professor goes on to explain how problems concerned with minimal surfaces can be studied with the help of soap films. The discussion lasts for about 25 minutes until he is catapulted out of the building by some strange amusement ride.
Yes, this is a mathematics video, really. The discussion of mathematics, although sometimes superficial and at other times too brief, is generally palatable. The computer-generated animation sequences involving these surfaces were truly amazing and certainly aided in the conceptualization of some complex mathematics. The video was claimed to be amenable to a general audience interested in science, but would also perhaps have educative value for more advanced students of mathematics (all the way up to graduate students of differential geometry). This claim seemed a bit absurd, seeing as it is difficult enough to teach a class in which the students' backgrounds do not differ by such a vast gap. So, to test whether this assertion might have some degree of validity, I showed it to my undergraduate differential equations class. Most of them found the area of study interesting, but the following negative comments were recurring:
The computer voice was annoying and hard to understand, and the music was too overpowering.
It was difficult to distinguish the information from the entertainment. I think some of the informative aspects of the video were overwhelmed by the "too cute" story line. Also, the length of the video could be decreased by 5 minutes if only the boy tip-toed faster.
I must say that I concur with these remarks. I have some background in elementary differential geometry and I still found it difficult to comprehend what the main points were, at times. It seems that the technology, although it works wonders, can be overwhelming and rather than having aided in one's understanding, it has hindered it.
The video does have some redeeming qualities and you can certainly tell that a vast amount of effort went into its production. However, in my opinion, it might be better suited for a high school (or even middle school) audience as a "motivational" device used to stimulate interest in mathematics. The creators provide a rather detailed booklet to accompany the video, as well as a link to a web site containing material related to the video (applets, animations, and the like).
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.
In comparison to the first video, this one is better constructed. The use of technology is effective and not overdone. It is half the length of the previous one and conveys the same amount of mathematics in an understandable manner. The music is not excessive, but does become rather boring near the end. A booklet summarizing the material presented in the video is also included.
Publication Data: Touching Soap Films: An Introduction to Minimal Surfaces, by A. Arnez, K. Polthier, M. Steffens, C. Teitzel. Springer VideoMATH series. Springer-Verlag, 1999. VHS/NTSC video tape, approx. 45 minutes, $38.00. ISBN 3-540-92635-6.
Arabesques & Geometry, by A. F. Costa and B. Gomez. Springer VideoMATH series. Springer-Verlag, 1999. VHS/NTSC video tape, approx. 20 minutes, $32.00. ISBN 3-540-92639-9.
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. His most recent work deals with abstract nonlinear nonlocal Cauchy problems in Banach spaces and integral equations governed by causal operators. 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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MAA Online is edited by Fernando Q. Gouvêa (fqgouvea@colby.edu). Last modified: Tue Jul 11 09:21:29 -0500 2000