A random walk through mathematics -- mostly through the random part.
Standard F Stops, sometimes you get partials like 2, 3.2 and 4. As your post implies F Stops double or halve the light projected on the negative, paper or sensor. Photographers use 'F Stop' to talk not just the opening and closing of the aperture but also the changing of the shutter speeds which also move by doubling and halving. I do wonder about f8 and f16, which are standard on all cameras and lenses I've handled.22.214.171.124.4 +5.6= 8115+11= 1622
They should have said "powers" not "multiples"
Yes, you're right.What they meant is that the LIGHT doubles or halves.
BTW everything in photography is log not just f stops; also film and paper sensitivity. There is a point where all that gets shelved and you expose, develop and print for your eye.You expose and develop a negative for the print you wish to make; no matter what is written every photographer messes around, even digital. Even without researching, I know the sensor's light sensitive will a be power, a log curve [right word?]. AND of cause you dump that on your compute and into Photoshop and use a log curve [curves adjustment layer] to adjust the image.I guess it shouldn't be surprising we are talking about light and its intensity.
ISO 216 paper sizes are in powers of √2. For example, A4 paper (analogous to U.S. letter size) is 210 mm wide, A5 paper (the next-smaller size) is 148 mm wide, and 210/148 ≈ √2. In general, A_k size paper is 841 · 2^(-k/2) mm wide and 1189 · 2^(-k/2) mm long.
Mark: the fascinating thing is why the paper sizes are in that ratio. I'm sure you know this, but it's also the aspect ratio of the papers themselves.That is, each size has sheets of the same "shape" -- they're all proportional -- and you get the next smaller size by folding a sheet of the current size in half.
I thought about mentioning that, but I decided it wasn't really on-topic, and that to bring it up would just be showing off.
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