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 $n=3$:

![arithmetic-geometric means inequality][1]


(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 the low quality, but I don't have 3d-ninja-rendering skills. 

  [1]: http://math.berkeley.edu/~dranjan/figs/ag_ineq.jpg