This post follows my video, The Bubble Sort Curve. You’ll probably want to watch that first. If not, you should at least be familiar with bubble sort. My video answers question, “What is the shape formed by these diagrams?” Normally for a problem this silly, I would be perfectly happy with a intuitive but non-rigorous argument like the one in my video. But for some reason I couldn’t rest until I had found a precise, mathematical way to state (and then solve) the problem. After spending more time...