Browsing by Author "Pengelley, David"

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    How efficiently can one untangle a double-twist? Waving is believing!
    (Springer, 2017-03) Pengelley, David; Ramras, Daniel; Department of Mathematical Sciences, School of Science
    It 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.