Quick question about aperture...

From what I understand aperture is a ratio of focal length to diameter of the diaphragm in the lens. So with a 50mm f/1.0 lens...is the opening of the aperture equal to the focal length? Is the lens 50mm wide as well as 50mm in focal length?

Also, how does this effect constant aperture lenses? How can this be possible across multiple focal lengths?

"The pupil diameter is proportional to the diameter of the aperture stop of the system. In a camera, this is typically the diaphragm aperture, which can be adjusted to vary the size of the pupil, and hence the amount of light that reaches the film or image sensor. The common assumption in photography that the pupil diameter is equal to the aperture diameter is not correct for many types of camera lens, because of the magnifying effect of lens elements in front of the aperture."

http://en.wikipedia.or​g/wiki/F-number