The name of this shape is an umbilical torus, and it has become a relatively popular tangible example of calculus over the years, whether on the covers of calculus textbooks or as a statue (a rather famous one is located at Stony Brook University). The simple explanation of this piece is that it is a single edged three-dimensional shape, something which at first thought might sound impossible. Naturally, to go along with this lone edge that wraps around the body of the figure three times uniquely (and infinitely over the same track) there is only a single side to this figure as well. These traits make it a particular fascination in the field of singularity theory. 

This shape has gained popularity due to its bizarre characteristics, but also its aesthetic draw, as it leads the viewer to engage in the mathematics of it as well. Upon my first viewing, I pondered whether it was even possible to create such a figure in a three-dimensional form, or whether it was simply an illusion. However, as this piece, and hundreds of other recreations of this geometric marvel have shown, it is possible, fascinating, and a remarkable example of the interaction between mathematics and aesthetics.

This piece was created for Chris Sinclair's HC 209H course, Math & Aesthetics.