This movie introduces cube knots—a new way to represent knots in 3-dimensional space. Cube knots are special because there are two Reidemeister-like moves that take any cube diagram representation of a knot to any other cube diagram representation of that knot.

Read the paper, “Cube diagrams and 3-dimensional Reidemeister-like moves for knots,” that started it all. The paper, joint work with Adam Lowrance, was published in the Journal of Knot Theory and Its Ramifications (volume 21 (2012) no. 5, pages 1-39).  Mathematica programs for manipulating cube knots can be downloaded at https://code.google.com/p/cubeknots/.

I would like to give special thanks to Justin Reusch for the animation, and Paul Schubach for the music! (Click the links to learn more about them.)

CHANNEL: Baldridge Theorems