Math with Balloons
In demonstrating what a mathematical knot is, balloons are the best medium that I’ve found. They have enough stiffness to keep the knot from collapsing so that you can’t see its structure (a string or rope would either be floppy and hard to work with, or you would have to pull the knot tight, which would make it hard to see it’s structure). They have enough give to allow knots to be tied in them. They are very visisble and the ends can be twisted together to complete the loop.
Here I am with not a knot, but a link: the Borromean rings. It has beautiful symetries that have been recognized for centuries and is important to low dimensional topology (in fact, an early incarnation of my dissertation featured the Borromean rings).