In mathematics, a knot is a single strand crossed over itself any number of times, and connected at the ends. The Reidemeister Moves have been proven to be the three core moves necessary to fully untangle a knot. We define a set of generalized moves based on the Reidemeister Moves which only reduce or maintain the complexity of a diagram. We provide a proof that these moves are sufficient for untangling all knots, including hard unknots. Additionally, we construct a computer program which reads the projection of a knot in its Extended Gauss Code notation and uses our moves to untangle it to the smallest possible number of crossings.


Moynihan, Matthew

Second Advisor

Sommer, Nathan


Computer Science; Mathematics


Geometry and Topology

Publication Date


Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis



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