Pengelley, DavidRamras, Daniel2017-06-302017-06-302017-03Pengelley, D., & Ramras, D. (2017). How Efficiently Can One Untangle a Double-Twist? Waving is Believing! The Mathematical Intelligencer, 39(1), 27–40. https://doi.org/10.1007/s00283-016-9690-xhttps://hdl.handle.net/1805/13291It has long been known to mathematicians and physicists that while a full rotation in three-dimensional Euclidean space causes tangling, two rotations can be untangled. Formally, an untangling is a based nullhomotopy of the double-twist loop in the special orthogonal group of rotations. We study a particularly simple, geometrically de ned untangling procedure, leading to new conclusions regarding the minimum possible complexity of untanglings. We animate and analyze how our untangling operates on frames in 3{space, and teach readers in a video how to wave the nullhomotopy with their hands.enPublisher PolicyArticle