Mathematical Experiment 11

  1. Construct an animation showing Steiner's porism:

  2. Construct an animation showing that if two circles c1 and c2 happen to have the property that c1 contains the centers of four circles G,H,I,J and c2 contains the points of contact P,Q,R,S of the four circles in the chain, then there are infinitely many such chains of four circles.

  3. Construct an animation showing all possible circles tangent to a given conic with center on the axis.

  4. Given a circle and a point on a fixed diameter, construct an animation showing all possible conics having the diameter as axis, the point as one focus and tangent to the circle.

  5. Construct the osculating circle to the parabola.

  6. Construct the osculating circle to the inversion of the ellipse and the hyperbola.
  7. Given complex numbers z and w, construct the product zw and the quotient w/z graphically.

  8. Construct the complex curve f(w) = w2 as w  runs over a circle, not necessarily centered at 0. Verify the drawing with Maple.
  9. Construct the tangent to the curve in the above problem. Recall that f¢(w) = 2w·w¢.