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RE: Mathematics as basis of beauty: Beauty is in the Phi of the beholder
I think it is kind of a philosophical question.
Can we calculate beauty?
Can we calculate all things in universe?
The golden ratio can be defined as the limit of f_n+1/f_n or with the definition in your post.
So is a human construction or a construction of nature or even god?
The masterminds behind the limits were Newton and Leibniz. Both were thinking about math in a metaphysical way, but with different ideas of human, truth and nature.
can we really calculate beauty?
Julian De Silva is a cosmetic surgeon who sometimes use golden ratio. and admit it, it makes his clients more beautiful. However, its still just a human perception, only suggesting what beauty should be. When you accept who you really are and contented for what you already have that's what makes you the most beautiful. :)