The advent of accessible automated tools — 3D printers, laser cutters, CNC-controlled mills, vinyl cutters, et.c. — that through the Maker movement reaches commodity prices opens up a number of new approaches to art: especially algorithmic and mathematical artworks. The computational control allows us to write algorithms to generate concrete physical art, and their precision allows a higher resolution than what the eye can discern.
In my mathematical art, I seek to reify the abstract, to make mathematical concepts and shapes available to touch, to trace, to twist and turn. To create physical artifacts meant for interaction to bring the complex closer and make the abstract concrete.
Three surfaces can be constructed by identifying opposite sides of a square. They are distinguished by twisting pairs of sides before gluing - like with a Möbius strip.
By twisting both pairs of sides, we construct the Projective Plane. Like the Klein Bottle, the Projective Plane cannot be represented in 3-dimensional space without self-intersections.
This particular shape, the Roman Surface, is a projection of an important construction from algebraic geometry: the Veronese Embedding.