This January the 2020 Joint Mathematics Meeting was held in Denver, Colorado. Every year the Art Exhibition at the Convention seems to get better and better.
I will present a small sampling of the work on display.
Anne Ligon Harding and Clayton Shonkwiler created this lino cut print featuring trefoil knots. The knots both have 3 fold rotational symmetry. The use of parallel lines gives the illusion of under and over in 3-D space.By flipping the prospective 180 degrees the viewer can see the trefoils from different angles. Having one knot on a white background and the other on a black background juxtaposes positive and negative space.
James Stasiak used the process of digital photo improvisation to create this print on metal. According to Stasiak a photograph of railroad tracks was manipulated using “tessellations and polar projections” to the form this striking image.
The gallery area at JMM was full of interesting work. Here are two more excellent examples.
Elizabeth Whiteley work is often related to botanical drawing and painting. In this new work she explores the geometry of of plants, but also the symmetries of design. Through her study of Frieze Group Symmetries she is developing a series of drawings that tackles the challenges that occur at the corners of the page. A Frieze Group is the mathematical classification for 2-D patterns that repeat in only one direction. Often seen on building as border decoration. There are seven symmetry groups that relate to Frieze patterns involving combinations of rotations reflections and translations.
The silverpoint drawing “Halesia carolina I” (above) features a central figure of three blooms surrounded by a border pattern of single blooms. This frieze pattern features reflected translations with a line of reflection at the center of each side. Whiteley’s drawings call to mind the decorative use of borders in illuminated manuscripts. By referencing the patterns of the central figure in the design element of the border, the symmetries become more connected to the central theme.
The clean lines of Clayton Shonkwiler’s digital animation “Rotation”drew my attention. Using circles and lines, the video presents undulating, almost sensual, geometric images.
I am providing a still shot I took in the gallery, but his videos are available on Shonkwiler’s website.
Although the geometric figures, circles packed into the square grid of the video frame, are basic, the mathematics for this visual feat is quite complex (Shonkwiler utilizes a Möbius transformation of the hyperbolic plane to the Poincaré disk model). I think it is the purity of the clean lines of the circles that allow the grace of the more complicated mathematical processes to translate into a really beautiful video.