Knot Theory

Two diagrams represent the same knot if one can be transformed into the other through Reidemeister moves, or if you can make a looped string look like each of them. Can you match physical knots to their diagrams? Can you tell which pairs of diagrams represent the same knot?

Video:

• A video from Numberphile about knots: https://www.youtube.com/watch?v=aqyyhhnGraw

Additional resources:

• Wikipedia article on Knot Theory: https://en.wikipedia.org/wiki/Knot_theory
• Quanta article about why knots are important: https://www.quantamagazine.org/why-mathematicians-study-knots-20221031/

Fun quote:

“In the 1860s, Lord Kelvin’s theory that atoms were knots in the aether led to Peter Guthrie Tait’s creation of the first knot tables for complete classification. Tait, in 1885, published a table of knots with up to ten crossings, and what came to be known as the Tait conjectures.”