Bow Wow

The President has his problems with the etiquette of the bow. The problems are so bad one might characterize him as having a bowing disorder.
Bows can be generally divided into three main types: informal, formal, and very formal. Informal bows are made at about a fifteen degree angle or just tilt over one's head to the front, and more formal bows at about thirty degrees. Very formal bows are deeper.
How many times did he just bow?
Generally speaking, an inferior bows longer, more deeply and more frequently than a superior. A superior addressing an inferior will generally only nod the head slightly, while some superiors may not bow at all and an inferior will bend forward slightly from the waist.
Everyone remembers his bow to the King. Some say the American president shouldn't be bowing to foreign royals - something about Democracy, I think? That was true in the old days, maybe - but with the President also the Chosen One, the rules seem to be different.