Allow me to introduce myself: I'm a mathematician.

Gedas was visiting Vilnius to register the birth of his second child. We went out for beers with Auriukas and Bronius. After a few beers somebody asked, for no reason in particular, "what's the sum of the internal angles of a hexagon?" The question wasn't addressed to anybody in particular but sort of as a rhetorical question, such as "Who is John Galt?" or maybe sort of as a general challenge. Irregardless of the meaning of the question, which was lost somewhere in a number of beers already drunk, I piped in with "720."

Nobody was expecting an answer, at least not one instantly. If the point of the question was a challenge than it was assumed that if would be a difficult challenge requiring four heads to be put together. But that's not how it went down. I just answered it and three surprised faces turned to me and two of them proceeded to call me a fool while the other demonstrated on paper that, in deed, I was right.

As the beer flow continued and the pipe smoking began, a new question was quickly put forth, two questions really: why is it 720º, and what is the formula for the internal angles of a polygon? I couldn't answer either. I just knew! Gedas was especially insistent that the meaning behind the knowledge is more important than the knowledge itself--why oh why is it 720º??? I didn't know how I knew it.

I asked the bartender for some paper. We spent the next 45 minutes or so working out the internal angles of all polygons up to an octagon, trying to work out the formula, and drinking several more beers. By the end of this period, which everybody else in the bar spent chatting about sports and women, or else shopping and men, the rest of my company gave up. I couldn't give up, though, I knew I was so close. Finally five minutes later I got it: 180(n-2) where n is the number of angles, happiest moment of my life excluding love life. Hooray!