Interesting. Is this how you calculate normal focal length lenses for the way you see? You calculate the hypotenuse of the square of the long edge of the format you shoot?
No, no and no again. The idea "normal lens" reflects two conventions.
The first, used in all still camera formats except the cine camera-derived 18x24 (single frame in cine parlance, half-frame in still photographer) and 24x36 (double frame in cine, full frame in still) is the gate's diagonal. Diagonal, not hypotenuse. Rectangles have diagonals, right triangles have hypotenuses.
The second, used with still cameras that use 35 mm film is arbitrary and reflects cinematographer's practice. Edison format (yes, TAE invented the motion picture industry) is 24x18 and the so-called normal focal length for the format is 50 mm, not 30 mm, the format's diagonal. This was adopted to keep the cine camera off the stage. It was retained by Barnack when he made an exposure tester for cinematgraphers. The original Leica camera was developed from the exposure tester. And that's why people who shoot double frame 35 mm take 50 mm as normal rather than 43 mm, the format's diagonal.
These conventions have been accepted since the beginning of photographic time. To avoid confusion, accept them and don't trip over each other trying to explain them. They're conventions and that's all, don't follow from laws of nature. Honor the conventions and people will understand you. Don't honor the conventions and you'll spread confusion. Ever widening circles of confusion.
Interestingly, in the late '50s through late '60s 35 mm SLRs were offered with "normal" lenses as long as 58 mm. This because the 6/4 double Gauss lens type that is the basis for nearly all of the fast "normal" lenses for 35 mm SLRs of that era is somewhat telephoto, i.e., has a shorter back focus than expected given focal length. Until SLR manufacturers managed to compute 50 mm 6/4 double Gauss types with long enough back focus to clear their cameras' mirrors and good enough performance they simply offered "normal" lenses with enough back focus. As I said, convention and nothing more.