What's the minimum turning radius of a vehicle, rectangular in shape, with length l units and width w units? One key point to consider, would be that, the inclination of the front wheels can be varied continuously(from 0 to 45 degrees - in both directions) while taking a turn(expert drivers do that all the time and can turn a vehicle in a very short space.).
This is not a homework problem. It's a problem that popped in my head, due to my own parking woes! As such, I am not sure, that the data given would be enough to solve it. So readers are welcome to improve the question(i.e they can suggest additional constraints or data that needs to be given).
While I've previously taken an analytic geometry course in high school, I've never attempted a problem like this. In college,(being an electrical engineering student) my analytical geometry education was not as comprehensive as that of a mechanical or civil engineering student. So I've no idea how to proceed.
This is the first in a series of parking problems, that popped in my head! Some of the other problems require more careful wording, so I've delayed their posting.
PS: When I say turning radius, I am referring to the wall to wall turning radius, as defined in the wikipedia entry on 'Turning Radius'. Also see this - http://firechief.com/apparatus/firefighting_turning_circles
EDIT: In case you can solve this question for any particular set of costraints, do proceed. Just make sure that you mention what those constraints are. Hopefully, someone else might be able to generalize. In case you need additional data, you can assume that data - again just state your data assumptions, so that others can understand.