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 $n=3$:

![(there should be a figure here...)][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 $k=1,\ldots,n$. 

(I made this in [Inkscape][2], a wonderful free-software vector drawing application. For the inequality and associated labels, I used the [textext][3] extension.)


  [1]: https://i.sstatic.net/dkoCZ.png
  [2]: http://www.inkscape.org/
  [3]: http://pav.iki.fi/software/textext/