[The word beautiful has its origins in the greek word “hour.”](http://en.wikipedia.org/wiki/Beauty#Etymology) According to the etymological interpretation the original meaning has to do with “something being in one’s hour”.
I think this is a very fitting view on beauty. People who represent exactly what they are at any given point in time — not representing more and not less and thus being totally congruent within themselves — definitely have an aura about them that could be called beautiful.
I can also extend that to finding ideas or solving problems. Once whatever you’re trying to find is full and ready and everything falls into place, it makes itself known and visible in a beauty that transcends the mere visual aspects of the word.