Mathematical Experiment 11

  1. Perform a simulation of a random walk on a graph with eight nodes. When reaching a node v, the probability of reaching the next node w equals 1/k if w is among the endpoints of one of the k edges leaving the node v. A bar chart indicating the frequency of the visits at each stage should be included.
  2. Draw the Moebius band.
  3. Simulate the solution to the planar ``three body'' problem.
  4. Demonstrate the proof of the Pythagorean theorem in the form of a movie. There are 256 proofs of this theorem given in Elisha Scott Loomis, The Pythagorean Proposition.
  5. Draw a trefoil knot.