Mathematical Experiment 10

  1. Trace the path of a light ray reflected inside a semicircular region.
  2. Suppose that a right cone with reflective surface sits on a flat checker board. Describe what appears when looking along the axis of the cone from infinite. What appears when looking from a finite distance? What appears when the eye is located at vertex of the cone?
  3. On the square net of the plane such as

    4. if the line ab is folded upon the line ac the result is a cone with vertex angle 3p/2. Draw the appearance of the cone when the vertex is directed toward the observer. This constitues three families of geodesics of the cone, each cutting the curves of another families at right angle. Do the same when the vertex angle is p and also the case the vertex angle is p/2. (Reference: H. Steinhaus, Mathematical Snapshots.)