I was trying to get a better intuition for "the curse of dimensionality" in machine learning, and needed to know the volume of a unit n-sphere -- so I remembered how to derive it. This derivation is quick, easy, and cool, and I want to share it with the world :) There is a long version of this derivation where I fill in the details that didn't fit into the 3 minute time frame, you can see it at http://youtu.be/eEJtMFdkzzU.