Latitudinal and Longitudinal Lines on a Sphere

$$\text{Flying a Plane}$$

=== You just started a new job as an airline pilot - congratulations! For your first flight, you take off from Amsterdam and fly 1000 miles due south. Then, you turn the plane and fly 1000 miles due west. You turn again and fly 1000 miles due north, and finally turn and fly 1000 miles due east.