Hyperboloid Hyperbole

2021

 

You wouldn’t think that two simple straight lines could entwine to sweep out so much geometric complexity.

 

This sculpture comprises two straight lines, set at particular angles and arranged to rotate. When in motion, each line defines a three-dimensional surface in space by moving, or sweeping, through it.

Hyperboloid surfaces are the product of rotating a two-dimensional hyperbola around an axis, sweeping out the surface of a three-dimensional figure. An amazing property of a hyperboloid is that it can also be generated by rotating a purely straight line set at an angle, which is how this piece works. Here, the two lines each sweep out hyperboloids, both separate but sharing the same mathematical principal axis. From the viewer’s perspective, the combined swept surface of the entwined hyperboloids evolves in complexity as the relative rotation of the two lines changes.

 

Two simple lines, in their dance, can entwine through space with graceful complexity. It’s almost astonishing, but such claims, of course, border on hyperbole.