Talia Blum

Undergraduate Student
Mathematics Department, Massachusetts Institute of Technology
Cambridge, Massachusetts, USA

I am interested in breathing life into mathematical objects through art. This work aims to illuminate intricacies in the construction of the Alexander horned sphere by comparing it to the humanoid. The sphere itself is simply connected, whereas the exterior is not. The piece invites the viewer to ask practical questions about the implications of these topological properties, as well as arbitrarily many pants.

Alexander horned sphere wearing pants
28 x 36 x 2 cm
Oil on canvas

The Alexander horned sphere wearing pants is constructed as follows. We begin with a torus, and remove a radial slice. Put pants on the sphere, where each horn acts as a leg. Connect a torus to the end of each horn, interlinked with the torus on the opposite horn. Repeat for each new torus added.