The animations for the hypocycloids has been
moved to the Parametric Equations 2 Space page for obvious reasons
Theoerm Suppose f(x) is continuous on [0,1]
and f(0) =f(1) Using the Intermediate Value Theorem Prove that for n > 1 there is at least one point c in [0,11/n] such that f(c+1/n) = f(c)
Proof Using IVT
The following are my notes on the application
of Improper Integration applied to escape velocity and the Swarzchild Radius
Escape Velocity
A history professor asked me to develop
animations to help explain to his class the Michelson  Morley Experiment . I'll not get into a discussion of the MichelsonMorley
experiment herethere are plenty of much better discussions than I could give. However, The following 2 animations are provided. The first is what happens when light is sent through an interferometer in a labaratory
at rest. Two beams are split and recombine in phase The
second is what was supposed to happen in a lab on earth as we move through the ether. The beams split and recombine out of
phase. Unfortunately,( or fortunately for
science), this didn't happen. The results were the same as the lab at rest result. The same result occured regardles of the orientation of the interferometer. The results of this "failed experiment" had tremendous implications
in modern physics including special relativity.
Lab at RestWhat happened
Lab in Motion What was supposed to happen
In The following 3 downloads is a scheme
for programming Mathcad to generate fractals from Julia Sets
Fractals
Dragon
Cloud
Generating Pythagorean Triples
