If you drew a dot on the edge of a wheel and traced the path of the dot as the wheel rolled one complete revolution along a line, then the path formed would be called a cycloid (shown below), combining both forward and circular motion.

If a wheel of radius 1 traces out such a path, what is the length of the path formed by one complete revolution?

That's not correct...

If you were to "unwrap" the wheel, you would find that this length is equal to the distance between the points where the red curve touches the ground.

What we are looking for, is the length of the curve itself, which is obviously longer than the distance between its two endpoints.

Posted by levik on 2003-06-23 07:46:13