*Z*-Squared Necklace
This is the signature piece for the art show "Surfaces Beyond the
Third Dimension"
,
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
.
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
.
This necklace theme was used in another piece within this exhibit, and was
incorporated into the AHSME 50th anniversary award
and an MAA recruiting poster in 1998. |