Geometric Constructions 8

  1. Demonstrate how the lemniscate can be drawn with the crossed parallelogram.
  2. Construct the lemniscate with a linkage different from the previous one.
  3. Design a linkage to draw the ellipse.
  4. Design a linkage to draw the cardioid.
  5. Design a linkage to draw the nephroid.
  6. Construct Peaucellier's linkage converting straight line motion to circular motion.
  7. Construct Hart's linkage converting straight line motion to circular motion.
  8. Construct two circles of the same radius with each rotating about a point not located at the center while remaining tangent to each other.
  9. Can you change the above construction to allow two circles of different radii?
  10. Instead of two circles tangent to each other externally, make the two circles tangent to each other internally.
  11. Construct two identical ellipses with each rotating about one of its two foci while remaining tangent to each other.