Volumes of n-dimensional balls

We all know that the area of a circle is and the volume of a sphere is , but what about the volumes (or hypervolumes) of balls of higher dimension? For a fun exercise I had my multivariable calculus class compute the volumes of various balls using multiple integrals. The surprising results inspired this post….

Flatland and other videos about dimension

Not long ago I watched the DVD of Flatland staring Martin Sheen as the voice of Arthur Square. The movie is based on Edwin Abbott Abbott’s 1884 book of the same title. Flatland is a story of polygons living in a two dimensional world and A. Square’s discovery of the third dimension. It is also…