Copy of Shortest Path Between 2 Points on a Sphere

In the context of a SPHERE, A GREAT CIRCLE is defined to be a CIRCLE that lies on the SURFACE OF THE SPHERE and LIES ON A PLANE that PASSES THROUGH THE CIRCLE's CENTER. In essence, the center of a GREAT CIRCLE and the center of the sphere are the same. Consequently, a GREAT CIRCLE also the largest possible circle one can draw on a sphere. In the applet below, the pink arc and blue arc make up a GREAT CIRCLE.


Note that the black arc and yellow arc (put together) DO NOT make a great circle. Why is this?

See below this applet for directions.

Directions: Move the 2 WHITE POINTS anywhere you'd like on the sphere. The PINK ARC is part of a GREAT CIRCLE of this SPHERE. You can move the YELLOW POINT anywhere you'd like as well. Again, note that the YELLOW ARC is NOT PART of a great circle. Slide the slider slowly and carefully observe what happens.


How would you describe the SHORTEST DISTANCE between 2 POINTS along a SPHERE? Explain.