Parallel Parking at Rigorous Trivialities

At Rigorous Trivialities, a relatively new math weblog, there is a post that is an early contender for the title of Most Important Blog Post of All Time. It’s a sketch of a rigorous proof that parallel parking is always possible (assuming the space is longer than your car). So if you can’t fit your car in that space, it’s your fault. Mathematics demonstrates its practical usefulness once again.

The post’s argument relies on an appeal to Lie algebras. If you take infinitesimal versions of the two basic motions of a car — turning the steering wheel and going forward — these generate a Lie algebra. Contained in the Lie algebra is the vector field that corresponds to going sideways. This implies that you can parallel park any car if you can switch between going forward and turning rapidly enough.