A Question of Balance
Take a piece of cardboard cut to some very irregular shape and endeavor to balance it on the end of a pencil. You will have to try a good many spots before you find the one that gives you a true balance. Of course, if you are dealing with a square or a circle, it will be easy, because you will try for the centre. Here it is far from simple, since the shape must be very irregular.
There is a very neat little way of doing it, however. Suspend the card by attaching a piece of cotton to the edge, selecting any point you like. While the card is hanging, draw a line across it which is the line of the hanging thread prolonged. Next, support the card in exactly the same way, but from another point on the edge. Again draw a line across the card which is the line of the hanging thread prolonged. Where these two pencilled lines cross is the centre of gravity of the card and, at that point, the pencil will support it.