confusion.

[d4170n]

I was reading an article on f stops. it said that aperture f stops double and halve just like stops in iso and shutter, but they double and halve in area.
this all makes since until i thought about zoom lenses and stuff.
here is the article.

http://www.uscoles.com/fstop.htm

can someone explain this to me any better?

its about the 6th paragraph down in the article

[Pistach]

I can tell you where the root of this confusion lies. Then to be precise one should carry out a lot of tedious computations. Because zoom cannot compete with primes, why bother? You have here another good reason to stick with primes.
Anyway, the correct formula for f stop is the ratio f/d where f is focal length and d is the diameter of THE ENTRANCE PUPIL. Things gets complicated because zooms have a variable geometry and thus he entrance pupil should be calculated for each configuration and, yes, each diaphragm.
Hope will help

[Pistach]

In other words, we must presume tha the changes in focal lenght are compensated by the effect of changes in geometry on the diameter of entrance pupil.
Hope I stated it more clearly