Here's a proof of the inequality of the arithmetic and geometric means in the form $$\frac{x_1^n}{n} + \cdots + \frac{x_n^n}{n} \geq x_1\cdots x_n.$$
Proof for $n=3$:
(
The "figure" for general $n$ is similar, with $n$ right pyramids, one with an $(n-1)$-cube of side length $x_k$ as its base and height $x_k$ for each $k=1,\ldots,n$.)
Sorry about k=1,\ldots,n$.
(I made this in Inkscape, a wonderful free-software vector drawing application. For the low qualityinequality and associated labels, but I don't have 3d-ninja-rendering skills. used the textext extension.)
