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I am glad I viewed Acorn Media’s “The Life and Works of M.C. Escher” before this tape. Although the tapes overlap a bit on the biographical details, “The Fascinating World” gives a much deeper insight into Escher’s art. Particularly interesting are the analyses of some of his more famous tessellations, made more comprehensible by rotating transparent outlines around pivot points to show how the artist planned his patterns. Particularly interesting is the explanation of his false-perspective prints by Penrose, who claims to have (with his father) given Escher the idea. And wait until you see the three dimensional versions of the “impossible” shapes, one of which showed up in the recent and lamentable “The Avengers” film: the steps that always go up! The only annoying feature is the English narration given over the Dutch and Italian “talking heads,” some of which are a drier than needs be; but such is the stuff of documentaries. I strongly suggest every math department in high schools and colleges purchase this tape for geometry classes as well as art departments to give the students a challenge of a different sort.

Maurits Cornelis Escher was an amazing artist as well as a superb applied mathematician. His figures apply various forms of symmetry in ways that can keep you looking for hours, at the end of which you will find yet another pattern inside those you saw when you first looked. While somewhat primitive, the computer animations of the figures allow you to better visualize how the figure was constructed.
The most illustrative techniques are when the narrator uses a simple device of a tack in the figure. This allows the narrator to rotate a figure around the tack, which demonstrates how the figures are symmetric in alternate quadrants and equal in quadrants separated by one.
Many of Escher�s figures are based on what are called impossible figures. These are geometric structures that cannot exist in three-dimensional space, but can be projected on a two-dimensional surface. Roger Penrose narrates this portion, demonstrating that sections of the figure are possible, and if it is cut and rotated the right way, appears to be a different figure. I enjoyed this a great deal, finally learning how Escher�s famous print of the endless waterfall was constructed.
Mathematicians and artists can appreciate this tape and it should be in every academic library. This is the best example of the marriage between art and mathematics that I have ever encountered.

Published in Mathematics and Computer Education, reprinted with permission.
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