And, really, what more "proof" do we need at Christmas?
(Cue Josh Groban, singing Believe)

I wrote this proof on the blackboard my first year teaching in an 8th grade honors math class in the last five minutes of class on the day before Christmas break.
Strangely, now that I teach in high school, I haven't been able to use it as I'm never at the right point in the curriculum for them to follow the "logic".