### Explanation of the Applet Quasiperiodic

We deal with a parametrization of a plane curve (x(t), y(t)) with both
components x(t) and y(t)
x(t)=a1*cos(2pi*t)+a2*sin(2pi***w***t)

y(t)=b1*sin(2pi*t)+b2*cos(2pi***w***t)

being quasiperiodic with frequencies 1 and **w**. The parameter **t** runs from 0 to
**tE** with ** stepsize dt**. If dt is
small, you see the "real" curve (you can try it, but you should reduce
tE also). The most impressing pictures you get for those **dt**
which are close to a rational number with small denominator.
dt may be varied by using the scrollbar.

You could start with a circle which you get by setting **a2=0=b2,
dt=0.01, tE=10**. Then you may increase a2 and b2 with
**w=5**. You will see symmetric closed curves. Now study
**a2=b2=0.5** and **a2=-b2=0.5**. Watch and explain the
difference!

In general you will get nice pictures if you choose **w** close to
a natural number and **dt** close to a rational number wirh small
denominator.

Enjoy it!