# Reidemeister's Theorem

(Advisor: Josh Greene)

From 2014-2015, while working on the BA Thesis in Mathematics, a kinetic sculpture was formed to study “singularities” in the projection (shadow on the wall) of a knotted circle in an acrylic sphere. An iPhone flashlight was placed to pass through the center of the sphere and a marker was place right in front of the sphere with its height and position coinciding with the center of the sphere. The three types of singularities are indicated in the diagram below and occur in a local region of the projection. Whenever a singularity appeared, a dot was formed on the sphere using the marker with its color corresponding to the singularity type.

Wood, acrylic

25 x 60 cm

Various knotted projections, each row determining a Reidemeister move in the shaded local circles (regions), and the middle projection in each diagram indicating singularities in the shaded circle.

There are three Reidemeister moves i.e. operations on a local region of a projection of a knotted curve. The middle local region in each row is the singularity each operation must pass through along with its corresponding color on the sphere.

Sketching the reality of the projections and the inaccuracies given by the shadows.