On this page will be pictures of sculptures I made in Fall 2009. I am on sabbatical during the Fall 2009 and Spring 2010 semesters. I have prepared three wax models for casting this fall, and I had the parts for one aluminum sculpture fabricated to my design by a local company, Crowley Fabrication, Inc., using a water jet cutter. I will put up pictures of the bronze castings after they are done. Here are pictures of the aluminum piece almost done.
In Summer 2009 I made a wax model of a sculpture based on the disks operad. It was inspired by sculptures of Robert Bosch, who told me how he had made sculptures using water jet cutting technology. He recommended that I contact a local company with that capability, if I wanted to have one made very precisely. I decided to make two versions of the disks operad sculpture, one cast in bronze and one fabricated in aluminum. The idea is to have disks cut out of a central disk so that any subdisk is a proper subset of any disk that contains it. I wanted the cut out disks to be able to rotate on an axis inside the space they had occupied, and I wanted that axis to be completely adjustible within that space. The design I came up with just required a groove to be cut on the inside wall of the cut out space, so that two spring-loaded watch pins, those used to hold a watch band in place, placed in holes drilled in the walls of the disk, would form the axes. The cutting of the disks was done by Crowleyfab, and I have been doing all the rest. Here are two pictures of the sculpture by itself, and two more showing it more polished and mounted on a simple wooden base. Note the thin inlaid aluminum line in the base on the right side.
I have carved another pentagonal torus with a 5-crossing knot, this time from a maple burl. This very light wood is characterized by its wild grain, which has many variations and intrusions. Here are pictures of it from both sides, two of the sculpture itself, and two more showing it sitting on a base, which is also made of maple burl.
Here are two pictures, showing both sides, of a version of this pentagonal torus which I carved from a block of striped ebony.
Here are pictures of three bronze sculptures I cast on December 4, 2009 at the sculpture studio at Binghamton University. Some are still in the process of being polished, and need some welding repairs for imperfections in the casting. The first is an alternating knot, but not the same knot made by the raised edge in the pentagonal torus sculpture shown above. This knot is made of solid bronze, hangs from a bent rod over a marble base, and has a wonderful tone when struck. It is a companion to another bronze knot sound sculpture I made before.
The next pictures show a new bronze Mobius Trefoil knot sculpture I have made, almost finished being polished, and mounted over a granite base using an arch similar to the one above. It has a very nice tone.
The next picture shows a bronze version of the disks operad sculpture, but the disks have not yet been mounted inside the open circles as they are in the aluminum version at the top of this page.
The next two pictures show a polished cocobolo wood carved torus whose cross section is a k=4 hypocycloid. The raised edge forms a knot which goes around the torus 4 times while going through the center hole 5 times, before coming back to its beginning. The parametric equations for this surface in cylindrical coordinates are: r = 4 + (2/3)[cos(pt)(3cos(s)+cos(3s)) + sin(pt)(3sin(s)-sin(3s))], theta = t, z = -(2/3)[sin(pt)(3cos(s)+cos(3s)) + cos(pt)(3sin(s)-sin(3s))], where s and t run from 0 to 2Pi, and p = 5/4.
While taking my daughter back to Oberlin College this semester, I visited Prof. Robert Bosch at his home. I enjoyed a wonderful afternoon talking about our common interest in mathematical art, and admired many of his sculptures. Here are pictures of two of his ``knothole sculptures" which I bought from him.
To see more types of sculpture I have tried, follow the following links:
Links back to:
Webpage of Alex Feingold,
Department of Mathematical Sciences,