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[Z-Squared Necklace]

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Z-Squared Necklace

This is the signature piece for the art show "Surfaces Beyond the Third Dimension" [Link], a collection of mathematical artworks by Tom Banchoff in association with several of his colleagues and students. Of the twelve pieces on exhibit, eight were ones done in conjunction with me, and four with students of his at Brown.

Here, we see five views selected from a sequence of projections of the complex squaring function from (real) four-space into three-space so that our two-dimensional view has three-fold rotational symmetry at each step. The view at the upper left is of the real part of the complex square seen from the positive z-axis. At the other end of the sequence is the real part of the inverse relation, the complex square-root, which appears as a doubly covered disk when seen from the z-axis. In between are views that occur as we rotate from one viewpoint (in four-space) to the other. More details about this image are available at the art show's web site [Link].

My role in this project was to go from Banchoff's original instructions ("I'd like a sequence of five views from this sequence") to the final product, which involved choosing the coloring, the lighting, the spacial arrangement, and the views to include, as well as working out the technical aspects of putting it all together.

This image was used (in black and white) on the invitation postcard for the exhibit, and later (in a rotated form) on the cover of the Notices of the American Mathematical Society in November 1996 [Link]. This necklace theme was used in another piece within this exhibit, and was incorporated into the AHSME 50th anniversary award [Link] and an MAA recruiting poster in 1998.

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Created: 08 Sep 2001
Last modified: Jan 6, 2002 10:36:38 PM
Comments to: dpvc@union.edu
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