Math Art

Shortly after college, I realized that trigonometry and linear algebra were at the core of almost every field that interested me in technology and science, including vector analysis of aggregate behaviors in the social sciences. While studying power transfer in AC circuits, just for fun, I found myself grasping for a better visualization of trigonometric relationships to improve my intuition when applying the math. It struck me to loosen my grip on the 2D geometry of the sine and cosine functions and instead focus on the 3D helix that generates the 2D projections we recognize in these functions. I created a helical model out of brazing rods fitted inside a clear box to sit on my desk for inspiration while writing my own 3D graphics rendering software, also just for fun.

A few years later, one of my coworkers at Berkeley Systems Software was working toward her passion to become a professional dancer. She teamed up with a UCB physics professor and her dance mentor to choreograph an illustration of superconductivity. Their project went on tour and was featured in a PBS Nova documentary featuring both the physics concepts and the value of interdisciplinary collaboration to break new ground. The relevance to my story is that her interdisciplinary success and a mispronunciation of her name introduced me to properties of the vesica pisicus and led me to replace the helical rods in my models with sheets of nickel cut into lens shaped sections sections bent in a single dimension so that they could be soldered at perpendicular edges.

The resulting sculpture immediately draws the eye to the 2D sine and cosine components of this 3D object. Upon closer inspection, it surprises people to see that this unusual shape will roll freely across a flat desk. This realization emphasizes that its edge forms a spring-like helix and that the shape of the familiar 2D waves derive entirely from the circular shape in the third dimension that gets lost when projected in 2D across the circle’s axis. Conversely, a 2D projection looking down this axis hides the wave and only shows the circle.