Back in the day, I was asked to take 2 weeks to learn Perl, before being assigned to work on some Perl based report scripts.

Since I needed a goal, I grabbed a sample script that echoed back on a socket, downloaded some RFCs, and chiselled out myself a webserver that could facilitate posting offers and accepting resource trades for a forum game. (Naturally, it worked great for any browser except IE)

I don't know if that counts as reinventing, as I certainly wouldn't want to offer it as an actual thing to use normally, but it rolled despite the primitiveness and I learned a lot making it on my own!