On this page are pictures of several sculptures I started in Fall 2008 and continued working on during Spring 2009. The bronze pieces were done in one bronze pour on November 14, 2008. These pictures show the pieces not completely polished, but will be replaced by other pictures when polishing is done.
On other pages I have shown various knots I have made of bronze and of steel, with various kinds of cross-section, twisted so that the surface has only one side and one edge. Here I show a large figure eight knot (20"x18"x12") whose cross-section is a hypocycloid. This piece is displayed hanging over a granite base from a 1/4" bronze rod bent into a parabola, in a way similar to the display of the bronze trefoil knot completed in Summer 2008. It is also a kinetic sound sculpture, and has an excellent ringing tone when struck.
In Summer 2008 I completed a Bobinga Brazilian wood carving of a torus with a pentagonal pattern coming from an embedded knot on the surface that goes around once, through the hole 5 times before closing. As a knot in space, the raised edge is actually just a circle (not knot), but embedded on the surface of the torus it cannot be contracted to a point, since it is homologically nontrivial. I made a bronze base for it, and the following picture shows the piece displayed on its base.
In May 2009 I carved a Cocobolo version of the same pentagonal torus which is about 5.5" wide. The grain and color of this wood is more dramatic than that of the Boblinga. I also made a small base of cocobolo to hold and display the piece in a vertical position.
I also made a bronze version of the same pentagonal torus which is about 6" wide.
I have made a bronze umbilic torus (7"x6"x2"), that is, a torus with hypocycloid cross-section, which should be compared to those I have carved from Cocobola Brazilian wood. This picture shows the piece much more polished than earlier pictures, but it is still not fully polished.
I was inspired to try making a version of the beautiful sculpture of Brent Collins ``Pax Mundi", which seems to me like a curved road around the world, set on a base shaped as a cone. Mine came out with many holes which will need a lot of welding repair, but here are some pictures of what it looks like before repairs. Eventually it will sit on the base in a different way than shown here.
The final sculpture shown here is a knot coming from a curve that goes around a circle three times before connecting back to its beginning. This is similar to a trefoil knot with three rods which I attempted before, but I don't think this is the same. What do you think? I made a base of marble so the sculpture hangs from a bent bronze rod, and when struck by a short bronze rod it rings like a bell, giving a very nice tone. This picture shows the piece more polished, but it still needs some welding repair and final polishing.
To see more types of sculpture I have tried, follow the following links:
Links back to:
Webpage of Alex Feingold,
Department of Mathematical Sciences,