How efficiently can one untangle a double-twist? Waving is believing!
| dc.contributor.author | Pengelley, David | |
| dc.contributor.author | Ramras, Daniel | |
| dc.contributor.department | Department of Mathematical Sciences, School of Science | en_US |
| dc.date.accessioned | 2017-06-30T15:00:14Z | |
| dc.date.available | 2017-06-30T15:00:14Z | |
| dc.date.issued | 2017-03 | |
| dc.description.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 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. | en_US |
| dc.eprint.version | Author's manuscript | en_US |
| dc.identifier.citation | Pengelley, 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-x | en_US |
| dc.identifier.uri | https://hdl.handle.net/1805/13291 | |
| dc.language.iso | en | en_US |
| dc.publisher | Springer | en_US |
| dc.relation.isversionof | 10.1007/s00283-016-9690-x | en_US |
| dc.relation.journal | The Mathematical Intelligencer | en_US |
| dc.rights | Publisher Policy | en_US |
| dc.source | ArXiv | en_US |
| dc.title | How efficiently can one untangle a double-twist? Waving is believing! | en_US |
| dc.type | Article | en_US |