Construction and enumeration of Franklin circles
Around 1752, Benjamin Franklin constructed a variant on the popular magic squares and what we call a magic (a, r)-circle. We provide a definition for magic (a, r)-circles, magic a-circles and, more specifically, Franklin magic a-circles. In this paper, we use techniques in computational algebraic combinatorics and enumerative geometry to construct and to count Franklin magic 8-circles. We also provide a description of its minimal Hilbert basis and determine the symmetry operations on Franklin magic 8-circles.