By taking two identical pieces of paper, crumpling up one and placing it anywhere on the second piece of paper you are guaranteed to have some point in the crumpled up mess that is over the same point on the flat piece of paper if you unfolded it again. Another explanation is here.

So I wanted to post my findings on the intermediate value theorem! You have to scroll down a little bit, but I found really interesting the part about the world having two antipodal points exactly the same temperature.