A proof of the identity $$1+2+\cdots + (n-1) = \binom{n}{2}$$

[![proof without words][1]][1]

(Adapted from an entry I saw at [Wolfram Demonstrations](http://demonstrations.wolfram.com/), see also the [original faster animation](https://i.sstatic.net/ouYCv.gif))


  [1]: https://i.sstatic.net/yKLqg.gif