Date of Award
Master of Science (MS)
Department of Mathematics
Knots are used everyday by all people, mathematicians and non-mathematicians alike. There are certain subsets of people that use knots more frequently than others such as sailors or members of the Scouting Movement.
A mathematical knot is a subset of 3-space that is homeomorphic to the unit circle. A knot used in non-mathematical circles is generally considered when two strings, etc. are wrapped around each other, with the ends potentially hanging. We introduce and explain through examples 1) how mathematical knots differ from general knots; 2) how mathematical knots differ from other mathematical knots via methods of deformation, colorability, and polynomials; 3) apply mathematical methods of knot determinations to practical knots to see how practical knots might behave as mathematical knots.
Sanchez, Andres, "Scouting Knots Are Not the Same Knots When Knotted" (2021). Theses and Dissertations. 1504.