Party in the 5th dimension #tibees #hypersphere #math

There's something weird going on with this. It's the formula to find the volume of a sphere in any dimension. This is recursive, so to find the volume of a five-dimensional sphere, set n is equal to five, and it would be two pi r squared over five times the volume of the three-dimensional sphere. So here's a list of the formulas for spheres in each dimension up to ten. If we set the radius to one for each of them, we get a number for the volume, and can compare. Here's a plot of dimension versus sphere volume. It increases initially, but then peaks in the fifth dimension. It then drops off and tends towards zero. An infinite-dimensional sphere would have a volume of zero, and a five-d sphere has the greatest volume of all. So I guess that's where the party's at.