Making mathematical physics accessible with affordable materials

Abstract

I decided to studymeteorology after a frightening encounter with a severe thunderstorm in the spring of 2011. I declared a physics major the next fall, despite never having taken precalculus. Along the way I fell in love with math and physics in their own right. As a visual learner, much of my understanding came through deriving concepts by drawing, but my frustrations with the loss of information inherent to presenting 3D concepts through 2D means led me to first investigate the use of sculpture as a way of solidifying my understanding. After encountering Oliver Byrne’s 1849 illustrated version of Euclid’s Elements, I realized it was possible to create visual aids that simultaneously have enough pedagogical value for use in a classroom and enough artistic merit that they would not look out of place in the living room of someone with no mathematical inclinations. This led to my current workwhich focuses on the use of cheap and easily availablematerials to create beautiful but practical visualizations that serve as concrete, tangible illustrations of otherwise abstract, cerebral concepts in analysis and mathematical physics. Robert Sabuda’s elaborateWizard of Oz pop-up book was hugely inspirational as a poor student: the idea that such dynamic 3D illustrations could be created with a material as cheap, widely available, and humble as paper was powerful to me. While still in school, I began dabbling in paper engineering, excited I had found a sculptural media that I could easily afford. But even after I was no longer constrained by financial necessity, my fixation on cheapmaterials remained because, in imposing such restrictions onmyself, I was giving myself creative challenges that forced me to find novel solutions, some of which required the invention of entirely new sculptural techniques. Since graduating with a double major inmath and academic physics and a studio artminor inDecember 2016,mymaterial repertoire has grown to include plastic beads, embroidery floss, 3D printed PLA, clear plastic cocktail straws, motherboard washers, acrylic rod, Copic alcohol ink markers, their refill inks straight from the bottle, and Mylar plastic film. The combination of alcohol ink and Mylar has especially captured my imagination, and I have made it something of a mission to see howmany different topics in math and physics I can illustrate using the two. Among my favourite pieces borne out of this endeavour is this hanging mobile featuring six of the atomic orbitals of hydrogen (Figure 1), created using a sculptural technique of my own invention.