# Alex Feingold

Professor of Mathematics
Binghamton University, State University of New York
Binghamton, New York, USA

I am a Professor of Mathematics with a strong interest in Mathematical Art. I have been making mathematical art by carving wood, carving stone, and casting bronze and iron, and welding. The results of my efforts over many years can be seen on my university website under the section Mathematical Art by Alex Feingold". Recently I have been exploring how to make such art using 3D printing. My first goal was to recreate in jewelry size the Figure 8 knot with hypocycloid cross section (concave triangle) twisted 120 degrees as it goes around the path once, so that the resulting surface has just one side and one edge like a Mobius strip (1-Sided Mobius Figure 8 Knot). I like carving wood torus knots. See my 3D math art on my Shapeways shop.

Cast Bronze (3-5) Torus Knot Kinetic Sound Sculpture
43 x 50 x 24 cm
Cast bronze, sapele wood base
2010

This (3,5) torus knot was cast in bronze using the lost wax method at a foundry on the Binghamton University campus with help and supervision from Prof. Jim Stark of our art dept. The mentor and inspiration for all my mathematical art has been Helaman Ferguson, especially his umbilic (3,1) torus sculptures. I like the (3,5) torus knot because of its connection with the Lie algebra of type E8, which has been an important part of my math research. I have also been fascinated by the kinetic sound sculptures of Harry Bertoia, and this piece has a beautiful tone when struck. The knot itself is about 32cm in diameter, and is suspended from a parabolic arc made from a bronze rod. I have also made it as 3D printed jewelry 3cm in diameter.

Carved Sirari Rosewood (3,5) Torus Knot
14 x 14 x 3 cm
Sirari Rosewood
2019

This (3,5) torus knot was carved and polished by me from a block of Sirari Rosewood using a Foredom flexible shaft carving tool. The mentor and inspiration for all my mathematical art has been Helaman Ferguson, especially his umbilic (3,1) torus sculptures. I like the (3,5) torus knot because of its connection with the Lie algebra of type E8, which has been an important part of my math research. After the wood block was roughly shaped into a torus, a valley was carved into the surface following a hand drawn (3,5) knot, so that the knot becomes the peak separating sections of the valley as they both circle 3 times around the torus and 5 times through the central hole. I have also made this design by 3D printing as jewelry.