2019 is my 40th year of creating, designing, developing, and producing mathematical puzzles and games as an art form. Each set is researched, sometimes for years, to discover the many challenges inherent in its combinatorial tilings. Each set's theme and concepts, the mathematical principles that define it, are a paradigm of the marvels of the Universe, and so I design them with aesthetic, mathematical, and philosophical qualities that make them a joy to play and explore, inspiring the young and intriguing the most advanced scholar. I have dedicated most of my life to the making and selling of these "math-as-art" sets, and continue so with undiminished excitement in every new discovery.
An original design: 25 unique curved wedges, each one-fifth of a circle (golden ratio!), analogous to a Penrose kite, have 5 equally spaced ruler marks on their two straight sides. Each tile connects those marks in a different way, yielding all 25 permutations of paths. Match tile paths in groups of 5 to form 5 circles, or 2 circles of 5 and one longer wavy loop of 15 tiles. The largest figure joins all 25 tiles into a single closed loop forming one continuous path. The loop's shape can vary in many ways. I show here the one with largest enclosed area. This artwork replicates one of the solutions with a physical puzzle set (www.gamepuzzles.com/pentuniv.htm#AA). What would a loop with smallest enclosed area look like?