Alex J. Feingold
Professor of Mathematics,
Department of Mathematical Sciences,
State University of New York, Binghamton, NY
"Mathematics is the main inspiration for my sculpture. Many advanced
mathematical ideas can be expressed in sculpture, not just simple geometry.
I like best small sculptures that can be picked up and handled, so that the
tactile impressions are just as important as the image seen by the eyes. Surfaces,
edges, curvature and texture are the local characteristics felt, but the larger
global design appeals to the intellect and connects to the mathematics. I have
tried to incorporate motion and sound into my sculptures. My work is abstract,
not representational. I have been working mostly with the lost wax method to
create cast bronze sculptures, but I have also used carving and welding techniques
to create metal, wood and stone sculptures."
“ Genus 7 Torus Knot”
Bronze with Patina,
5.5" x 6" x 2"
A torus with 6 additional holes (3 vertical and 3 radial) forms a genus
7 surface. That surface has been
shaped to emphasize a single curve (knot) which runs around the torus
twice, going through each of the six
holes twice. Such a knot represents a highly nontrivial element of the
first homotopy group of the surface.
2007, Bronze Rod, 9" x 5.5" x 5"
“ Figure 8 Knot Rod ”
A bronze rod 1/4" in diameter was bent into a figure eight knot, and
welded into a continuous loop. This is the
next most complex knot after the trefoil knot, and its complement in
space has a hyperbolic structure. Simple but
elegant, this sculpture puts knot theory in your hands in concrete form.
2008, Bronze Cast, 9" x 9" x 6"
“ Hypocycloid Figure 8 Knot”
This picture shows the same figure eight knot as submission #2, but the
cross section is a hypocycloid curve
(the curve traced out by a point on a circle of radius R rolling with
out slipping in a circle or radius 3R). The
three vertices of the hypocycloid would trace out three circles on the
surface, but because of a one-third twist,
there is only one curve, and likewise, only one surface, not three,
making an object analogous to the famous
2008, Bronze Cast, 6" x 6" x 2"
“ Genus 3 Surface with Three Linked Knots ”
This piece is a torus with three pillars meeting in the center (like a
steering wheel of a car). The
surface is shaped to emphasize three separate curves which are embedded
in the surface, each of which go around
the outside of part of the torus, along a pillar, and back out, so that
they form three knots which are linked
with each other. They are symmetrically placed on the surface. After
being polished, I might want to apply a patina
to the surface, and then sand away the color along the curves so that
they stand out, as I did in submission #1, the
Genus 7 Torus Knot.