By Jillian Byrnes, Monique Dacanay, Kaycee DeArmey, Alana Drumgold, Ariyana Smith*, and Wisdom Talley*.
*Ariyana and Wisdom helped the group work through the problem set but were unfortunately unable to attend camp during the blog writing.
A mathematical knot is a loop in three-dimensional space that doesn’t intersect itself, and knot theory is the topological study of these knots. Two knots are considered to be equivalent if they can be stretched or bent into each other without cutting or passing through themselves. The simplest of these knots is known as the unknot, which is just a circle or its equivalence. Similar to a knot is a link, which is multiple knots intersecting each other. Both knots and links are often described in the form of knot diagrams, which are two-dimensional representations of the three-dimensional shape. There are an infinite number of both knots and links, but here are a few examples in diagram form: