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.
1.
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.
2.
How would you describe the SHORTEST DISTANCE between 2 POINTS along a SPHERE? Explain.