This demo displays a sphere and a curve on the sphere.
The length of the curve is given in a readout in the control
A hotspot P on the curve determines another point Q halfway
around the curve from P. A point M, which is the midpoint of P and
Q on the sphere, is displayed. A red great circle is displayed
with M as the north pole. If the length of the curve is less than
2π, the hemisphere will contain the curve.
Changing alpha rotates the half of the curve from P to Q around
the north pole M, thus demonstrating the proof of the lemma.