OT: Fibonacci Numbers Video

There is a complex set of trade-offs involved.

Peripheral vision is more effective to the sides than up/down. This is in part because, 'historically', threats were more likely to appear from the sides. The 'range of vision', _vertically_, is typically about +/- 60 degrees from the horizontal. However, 'to the sides', it is typically 80+ degrees from 'straight ahead', and in a significant number of people it can range to 90-95 degrees _and_more.

"Portrait" orientation (the long dimension vertical) is optimal -- in terms of 'visually pleasing', that is -- at 1.618:1. This ratio occurs 'naturally' in a bunch of aspects in the human body -- See da Vinci's figure studies.

"Landscape" is more natural, and 'panoramic', at a ratio that is 'wider' and 'flatter'. You don't get much from the extra 'sky' in an exterior shot. Similarly, for interiors, the floor-ceiling dimension tends to limit the usefulness of a greater display height.

Also, realize that 'wide-screen' in the movie theater is typically _1.88_:1.

and the famous 'Cinerama' process from the 1950s, 1960s, and 1970s, was

I don't doubt it. IIRC, the trickiest part is showing the limit exists, then the quadratic formula decides the value of the limit. Probably, the more general result can be obtained by using the original one: If you multiply the Fibonacci sequence by some any non-zero value c, then when you take the ratio of successive elements the c cancels out. So the sequuence 0, c, c, 2c, ... will yield the Golden Ratio too. Beginning with -1, 0 instead we get -1, 0, -1, -1, -2,.. and this also yields the Golden Ratio (discard the first term to see this). Taking the sum of the 2 sequences

Bill