What's the difference between a doughnut and a bretzel? How to hang a frame to a wall in a sneaky way? How to prove that a rope and metal ring puzzle is impossible to solve? How to be sure that the granny knot and the figure-eight knot are actually different? Those seemingly different (yet equally bizarre) questions have deep ramifications in Topology, and it turns out that to answer them, it revolves around using the same construction. Instead of going into the fuss of the algebraic details, we will give the rough ideas, accompanying them with pictures (after all, I have to stick to the cliché of the topologist!).
