Geometric Constructions 7

  1. Construct the formation of the envelope of light rays, emitted from a radiant point source at the cusp of a cardioid, after reflection by the same curve.
  2. Construct the tooth-wheel coupling between the deltoid and the 3-cusped epicycloid.
  3. Construct the tooth-wheel coupling between the deltoid and the cardioid.
  4. Construct the tooth-wheel coupling between the deltoid and the nephroid.
  5. Construct the tooth-wheel coupling between the deltoid and the astroid.
  6. Construct the tooth-wheel coupling between the cardioid and the nephroid.
  7. Construct the tooth-wheel coupling between the trochoids.
  8. Construct two identical cardioids each rotating about its cusp meeting orthogonally on the line segment joining the cusps.
  9. Let AB be a fixed diameter of a circle O. Through a variable point C on O construct two cardioids with AB and BC as tangents and with the cusps at the distance of 2AB apart.
  10. Construct similarly for a pair of nephroids.
  11. Construct similarly for the nephroid and the cardioid.