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]: http://web.archive.org/web/20131103014358/http://img64.imageshack.us/img64/5738/arithgeom01b.png [2]: http://www.inkscape.org/ [3]: http://www.elisanet.fi/ptvirtan/software/textext/