Breaking Chalk

Drop a dustless chalk, held horizontally, at a decent height (say eye level), on a hard surface. Most of the time, it breaks into 3 pieces. Well, it may not surprise you, but I was I knew this phenomenon when I was having a chat with one of my teachers in 2006. He told me about it, but he never proved it or explained it with support. I guess it was either too complex or lengthy.

Recently, I happened to come across some discussions on the net pertaining to breaking chalk.

Some say that the chalk will fragment to pi pieces--meaning 3 pieces and some finer bits.

Some plan to use computer simulation of falling chalk to aid them in the process of proving.

So why 3 or pi pieces?
I look foward to seeing the prove, if there is.

It is unlike Buffon's Needle, which has a solution using geometric probability which obtains: