Above: From Paris, 1927: a novelty car that can “sidle” into parking spaces.
Below: Someone was actually working on this in the 1950s (thanks, Martin):
A related puzzle from The Chicken From Minsk, Yuri B. Chernyak’s 1995 collection of math and physics problems: Why is it easier to parallel-park a (conventional) car by backing into the space rather than pulling in directly?
Imagine pulling out of the space. With the front wheels turned sharply to one side, the center of rotation is close to the car’s rear end; the front of the car swings out of the space, avoiding the car in front, and then the rear follows it. Because the center of rotation is so close to the rear of the car, it would be hard to back out of a tight space. Now play the scenario in reverse: By backing into the space, the driver is putting the least maneuverable end of the car into position first and can then rotate the rest into place.