I'm not sure what forum this should be in--is it a physics puzzle, a geometry puzzle, or an engineering puzzle? It seems to be all three, so I put it here. When you have a vehicle with two wheels and one of them is canted at an angle, and a circle can be constructed on the ground so that it has two points of tangency at the two wheels, and the lines of tangency at these points follow the directions of the two wheels, it is clear what circle the vehicle must turn in. Now consider a bicycle. You can't construct such a circle here; the point of contact of the front wheel falls on the line of the direction of the rear wheel. In one case, when the front wheel is turned at a right angle to the rear wheel, the circle the vehicle must turn in is obvious; the front wheel traces a circle with the bike's length as the radius, and the back wheel stays put. But when, say, the front wheel is at a 45 degree angle to the back wheel, how large a circle does each wheel trace?