The interplay among 2-dimensional geometric shapes offers a very accessible “art experience” for even the most art-phobic viewers. “I like it or I don’t.” “I find it interesting or I don’t.” This is true for pure geometric forms, like polygons, as well as for more representational forms, like stars. As a mathematical artist, I find it challenging to present simple but mathematically rigorous arrangements that will draw in the viewer with their visual interest, and then awaken the viewer’s mathematical appreciation “though the back door”.
This figure displays the five regular polygons of 4 through 8 sides in traditional rainbow order. The rules which govern this work are: equal area polygons, arranged in numerical order, connected by an inner line formed by one side of each polygon, which don’t overlap. If you add a sixth polygon, or start with a polygon of 5 or more sides, the last polygon will bump into an earlier one. This figure, along with the five- or six-polygon figures that start with a triangle, are the only three figures that comply with the rules. People who read from left to right (as with English), should find this figure “reads” comfortably from red to blue. This figure might present an uncomfortable feel for those who read in a different direction.