Andrew James Smith
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.
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.