In the context of a [color=#38761d][b]SPHERE[/b][/color], [br][br]A [color=#1e84cc][b]GREAT CIRCLE[/b][/color] is defined to be a [b][color=#1e84cc]CIRCLE[/color][/b] that lies on the [b][color=#38761d]SURFACE OF THE SPHERE[/color][/b] and [b]LIES ON A PLANE that PASSES THROUGH THE CIRCLE's CENTER.[/b] In essence, the center of a [b][color=#1e84cc]GREAT CIRCLE[/color][/b] and the center of the [b][color=#38761d]sphere[/color][/b] are the same. [br][br]Consequently, a [b][color=#1e84cc]GREAT CIRCLE[/color][/b] also the largest possible circle one can draw on a [b][color=#38761d]sphere[/color][/b]. [br][br]In the applet below, the [b][color=#ff00ff]pink arc[/color][/b] and [b][color=#1e84cc]blue arc[/color][/b] make up a [b][color=#1e84cc]GREAT CIRCLE. [/color][/b]
Note that the [b]black arc[/b] and [color=#bf9000][b]yellow arc[/b][/color] (put together) DO NOT make a great circle. Why is this?
[b]Directions: [/b] [br][br]Move the [b]2 WHITE POINTS[/b] anywhere you'd like on the [b][color=#38761d]sphere[/color][/b]. The [b][color=#ff00ff]PINK ARC[/color][/b] is part of a [b][color=#1e84cc]GREAT CIRCLE[/color][/b] of this [color=#38761d][b]SPHERE[/b][/color]. You can move the [b][color=#bf9000]YELLOW POINT[/color][/b] anywhere you'd like as well. [br][br]Again, note that the [b][color=#bf9000]YELLOW ARC[/color][/b] is [b][color=#bf9000]NOT PART[/color][/b] of a great circle. [br][br]Slide the slider slowly and carefully observe what happens.
How would you describe the SHORTEST DISTANCE between 2 POINTS along a [b][color=#38761d]SPHERE[/color][/b]? Explain.