Paul Salomon
My earliest love of mathematics came when I realized its utility in creating beautiful things. As a third grader (and ever since), I spent countless afternoons drawing stars and patterned shapes with a protractor or compass. In my work as a teacher I get to share that beauty in creation with my students. In my art I sometimes try to illuminate the complex structure and interconnectedness of simple, patterned objects. I'm compelled to understand complete spaces of related works and how my choices as an artist locate me within that space.
Stars of the Mind's Sky is the title of a series of works exploring the space of regular star polygons. Here we see 300 stars "in orbit" along concentric circles. The number of points on a star increases with the radius, and stars of a given number of points are spaced evenly along their circle according to "density," or the "jump number" used in generating them. Algebraically, these represent the subgroups and cosets generated by elements of a cyclic group. They have been colored on a gradient to indicate the number of cosets; a red star signifies a generating element. As a consequence of these structural choices, we may observe congruent stars with increasingly many cosets, shifting their way to blue along central rays through any red star.