Mathematical Experiment 11

Construct an animation showing Steiner's porism:

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.

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

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.

Construct the osculating circle to the parabola.

Construct the osculating circle to the inversion of the ellipse and the
hyperbola.

Given complex numbers z and w, construct the product zw
and the quotient w/z graphically.

Construct the complex curve f(w) = w^{2} as
w
runs over a circle, not necessarily centered at 0. Verify the drawing with
Maple.

Construct the tangent to the curve in the above problem. Recall that f^{¢}(w)
= 2w·w^{¢}.
exp11.tex