How efficiently can one untangle a double-twist? Waving is believing!

David Pengelley; Daniel Ramras

doi:10.1007/s00283-016-9690-x

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arXiv · 1610.04680

How efficiently can one untangle a double-twist? Waving is believing!

David Pengelley·Daniel Ramras

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Abstract

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 defined 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.

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David Pengelley, Daniel Ramras. 2016-10-15. How efficiently can one untangle a double-twist? Waving is believing!. https://doi.org/10.1007/s00283-016-9690-x

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