The
Gauss Map
of a surface associates to each

point on the surface its unit

normal vector.

In these studies, the Unit Normals

to the surface are used to create
a color mapping on the surface

which imitates the default
Mathematica

(lighting)/rendering model.

LightSources
{{{1.,0.,1.},RGBColor[1,0,0]},{{1.,1.,1.},
RGBColor[0,1,0]},{{0.,1.,1.},RGBColor[0,0,1]}}

In these studies, however, the color
calculations are done in CMY color space
and the background is white.

Stewart Dickson has written the
software to convert the Gauss-map of an object to
a
Mathematica-style surface color map.
Download here.

The texture image is parametrically

mapped along the knotted torus.

Color 3-D Printing was done by
Z Corporation. Download here.

## Logarithmic Spiral Snail

A snail shell generated in
Mathematica Download here.

The Seventeenth-Century French mathematician Pierre de Fermat wrote in the
margin of his copy of Arithmetica by Diophantus, near the section
on the Pythagorean Theorem (a squared plus b squared equals c squared),
"x ^ n + y ^ n = z ^ n - it cannot be solved with non-zero integers x, y, z
for any exponent n greater than 2. I have found a truly marvelous proof, which
this margin is too small to contain."

This was left as an enigmatic riddle after Fermat's death and it became a
famous, unsolved problem of number theory for over 350 years.
Andrew Hanson has made some pictures, and I have in turn made
sculpture, of a system analogous to Fermat's last theorem - a
superquadric surface parameterized in complex four-space.

We think that the mathematics of the n=3 case are similar to
Fermat's own proof of the n=3 special case.
Our pictures have lent some visual concreteness to the recent news of Andrew
Wiles' proof of the Taniyama-Weil conjecture, which implies the proof of Fermat.

The
Z Corporation
3-D Color Printer has a
Bit-Mapped, color image slice-based software interface to its
build process. This interface
makes the
Z Corp
machine the ideal platform on which to execute the
Fractal Zoom in Three Physical Dimensions -- and in color!
Stewart Dickson has written the
software to interface this data object to the
Z Corp
3-D Color Printer. Download here.

## Painted Vases

The artist has developed the

software to generate a Vase,

as a mathematical function,

and to map a color digital

image onto the surface as a

VRML
V2.0 file.

This file format is suitable

for output using the
Z Corp

Color 3-D Printer. Download here.

"Botty Shelly"

## The Surreal Thing

Newell's "Utah Teapot" as prepared for
3D printing with a
Magritte and
J. Turner Whitted-inspired faux
environment mapped to the surface.

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Response Form.

Or contact:
Stewart Dickson, Sculptor
110 N. Whipple St.
Fort Bragg, CA 95437 USA
(707)813-0385
MathArtSPD@gmail.com

Press Here
to go to Mathart.org home page.