I made the following realization which I find absolutely elegant.
Say you have a book lying face up on a table. You take the book and throw it up and it lands face up in a new position on that table.
I claim the following supprising statement.
"We can either rotate the book around some point on the table or slide the book along the surface so that it ends up in the same position after it has been thrown".
See if you can explain this phenomena.
It reminds me of the Brouwer Fixed Point. His application is very supprising. Basically if you have two identical sheets one on top of another. You take the top sheet crumble it any way and place it on top the bottom sheet. There is a common point shared to both. But this is something totally different.