SPOILER ALERT - Broken Spaghetti Solution in 2D

SPOILER ALERT - this is the solution to the broken spaghetti problem. If you are not familiar with the problem, it asks you to consider the probability, that when a piece of spaghetti is randomly broken into three pieces, those three pieces can form a triangle by being connected end to end. It's a charmingly simply problem to state, and not difficult to solve, but there are some pitfalls that await along the way, making it one of my favorite problems of all time. Take some time to consider it if you've never heard of it, and then come back here for an interactive solution. You can also check out my video solution in full 3 dimensional glory on YouTube at: https://www.youtube.com/watch?v=Tw4P60UtB18