Pythagoras falls into a deep sleep and dreams of all the progenies of his original idea. These paintings represent what he would have seen in the internal chalkboard of his mind. Pythagoras saw mathematics in everything; I agree.
Pythagoras of Samos (c. 570 BC – c. 495 BC) was a Greek philosopher, mathematician, music theorist, and someone who inspires my love of the polar coordinate system.
This system provides me with a framework for looking at relationships between equations and shapes, and developing visual models to express my ideas.
My favorite geometric progeny of Pythagoras is the limacon, a beautiful snail-like shape with an elegant interior and exterior curvature. This form was studied by the painter and mathematician Albrecht Durer (1471 – 1528), and I find its polar equation and geometric form fascinating as well as a perfect structure for telling different stories in my life.
The first story I explore comes from the poem “Song of the Seven Hearted Boy” by Federico Garcia Lorca. By playing with the polar equation for limacons, I create a representational model for the boy’s seven changing hearts.
The second story involves my varying two parameters in a limacon equation, rendering a graceful model of identity; a visual representation of Carl Jung’s continuum of consciousness.
In the third story, I see the geometric qualities of a limacon as the optimal model for explaining how two bodies orbit, find each other, and continue together over time. This mapping also describes how two humans move through life, trying first to find their other half and then to remain fused together over time. In my paintings, I represent the relationship between Achilles and Patroclus as two limacons, circling each other, trying to find - and ultimately create – one new orbit together.
In these paintings, I use the limacon model to imagine the boy in Lorca’s poem recognizing the continuum of consciousness, coming to an understanding of his own identity, recalibrating his orbit, and finding the other half to complete his own heart.
"In Balios and Xanthos, Schultheis beautifully captures the process of creating a surface of revolution from the limaçon curve. We glimpse how the single point of self-intersection in the limaçon produces an infinite set of points of self-intersection in the surface it produces. We also arrive at the realization that the distance of the curve from the axis it is rotating around affects the resulting surface. The longer we let Schultheis’ art permeate our mental imagery, the clearer our mathematical insight becomes. His images help us to form a surface that can be rotated, sliced, and manipulated in our mind’s eye. In the end, we arrive at understanding."
Allison K. Henrich, Ph.D., Associate Professor & Chair
Department of Mathematics, Seattle University