What is different about Geometry on a Sphere?
We want to demonstrate that geometry on the surface of an egg would be different from the Euclidean geometry you are used to in a (flat) plane. An egg is not quite shaped like a sphere, but its geometry has many features in common with that of a sphere. A symmetric, round sphere is easier to work with to demonstrate these features. The following applet demonstrates certain features of spherical geometry, in particular, the fact that there is no well-defined way to keep track of directions. See the instructions below it. But before you try the applet, stand up and do the following experiment: • Curl the fingers of your right hand into a fist, but leave your thumb sticking straight out. • Hang your right arm down with your thumb pointing forward. • Keep your arm straight throughout, and never twist your wrist unnecessarily. • Swing your arm up and out to the side. (Your thumb will still point forward.) • Next swing your arm forwards, until it points straight ahead. (Since your remembered
