It's amazing what pure boredom can do, hah. As a teen at an airport, I once proved the area of a circle by taking the angle of packed triangles to the limit of 0. Not perfect maths mind you, but I was chuffed at the time nonetheless.
As for 5:59:59, the problem occurs because 0 and 360 are both possible values instead of me excluding one from the other. I wasn't sure how to do that elegantly, so I just left it and walked away whistling.
/ahem/ "An exercise for the reader" /ahem/