Watch the solution of an interesting problem on Triangles on a sphere and learn how to solve it. You may try the problem yourself and then watch the video.
Suppose the earth is a perfect sphere. You are on its surface at point A. First, you walk 1 mile south, then 1 mile east and finally 1 mile north. And voila! You find yourself at point A again. Can you find such a point A on the earth's surface?
Hint: There are infinitely many such points!