2022 Joint Mathematics Meetings
Andrew James Smith
Artists
Andrew James Smith
Artist
Cambridge, Ontario, Canada
Statement
Fifty years ago, I began a body of pencil drawings based on polygons. I titled the opus Polygonum Progredi. My “Progressions of Polygons” were born out of a socio-political philosophy I developed. I characterized it by the phrase: “None, One, Some, Many, and All”. In the following decade, I compiled over 200 original related studies, and many subsequent versions and treatments. Most of the drawings imply an infinite number of polygons, from a triangle through a square to a circle.
Artworks
The Smithon Proof
50 x 50 cm
Archival Digital Print on Paper.
2021
THE SMITHON PROOF
During these topological studies, I imagined a composite of the Parents inside-out. What was the circumference would become the center and vice versa. I assumed that the sides of polygons would cause circles when turned inside-out. They would be tangent to the center (which was the Parents’ circumference).
It wasn’t until forty years later that I devised a graphic test to prove the accuracy of my result of turning the polygons inside-out. I cut the composite into 72 five-degree slices. I then turned each slice 180 degrees. As the colour segments above imply, the shapes would not be circles, but clothoid loops.
Though this exercise may be outside parameters of science, it influenced my naming it the Smithon.