Discuss “How Things Work: Mathematical Knots”

A knot, in the conventional sense, is an intertwining rope or string usually designed to tie objects (or shoelaces) together. Take a piece of rope, twist, pull, and loop it a few times and you get a hitch knot. Loop it again and you get a half hitch knot. Loop it some more and you get a cow hitch knot. Glue those ends of the rope together, however, and you get a mathematical knot.

A knot, in the mathematical sense, is a conventional knot on a closed loop. Stated another way, mathematical knots lack loose ends. This is a critical, fundamental difference between mathematical knots and the knots we tie every day. Regular knots can be easily untangled by manipulating the loose ends of a rope; mathematical knots cannot. Given this definition, a...