Hexagonal Parquet Deformations

I was commissioned to design a series of works based on classifications of hexagons.  I considered hexagon classes derived from symmetry: equilateral and equiangular hexagons with one, two, or three axes of reflective symmetry.  I expressed the variation within each class by designing parquet deformations, giving a static image that is full of motion and change.

Each one is a sort of tightly-arranged family portrait.

Sangaku

During the Edo period (1603-1867) Japanese people of all social classes created mathematical tablets called sangaku to be placed as offerings in Shinto shrines and Buddhist temples.  These tablets were meant for contemplative meditation and usually featured theorems or problems from Euclidean geometry.  During meditation, the geometric configurations were meant to suggest mathematical truth or perhaps a problem to be solved.  They serve as an inspiration to mathematical thinking.

With inspiration in mind, I created a series of sangaku to hang above my chalkboard, as meditative offerings to my students.

Compass Constructions

ratIt's sort of miraculous that simple, numberless tools like compass and straight-edge can create such beauty and perfection.  The images to the right comprise a rather in-depth study of the Platonic and Archimedean Solids -- ancient forms adored for their charming spherical symmetry.  Each is an orthogonal projection of a solid, along one of its axes of symmetry.

Yoshimoto Shorts

 Justin Lanier and I created a pair of stop-motion animated shorts to show off the properties of the Yoshimoto Cube.  The second short showcases a one-sheet cut-and-fold model I designed.  This model includes built-in paper hinges, an improvement on the usual tape, which wears and tears quickly.  The shorts were shown as part of the 2013 Bridges Conference Short Movie Festival in The Netherlands.

Stars of the Mind's Sky

Using a protractor to make stars was one of the first times I ever used mathematics to make something.  Decades later, I created a series called "Stars of the Mind's Sky" to explore and expose the beautiful structure among these stars.

I wrote Mathematica code to generate the first image on the right. The stars are arranged in concentric rings based on the number of points they have.  They are colored by the number of pieces they are made of – the Star of David being two pieces, for example.
More of my art can be found on instagram.