The most underappreciated formula

This talk centers around deriving the general formula for the volumes of spheres in higher dimensions. More broadly, it makes an attempt to take various initially counterintuitive facts about higher dimensions and make them (hopefully) a bit more intuitive.

Thanks to UC Santa Cruz for letting me film there, and to all its students for being such a lovely audience. Actually, the same thanks are owed to the International House at Berkeley, to the University of Wisconsin, and to Stanford. Not entirely intentionally, I ended up with a small de facto tour, giving this a couple of times.