You could use the Pythagorean theory to calculate how long and far it would take an enemy war ship to get to one place and help yourself choose the best course. You'd be able to make it to the destination before them and set a blockade to keep them away and make them retreat, possibly even surrender. You could also calculate how far and long it would take yourself to get the destination.
Another way you could the Pythagorean theory is by using it to see if you could beat your friend in a race to get a certain spot. Not to mention set up a slip 'n' slide for your friend and have them fall more than once. Or you could set up trampolines and jump from one to the next to help boost your time. Or you could always set up a hidden pit to stop your friend all together.