Math in Nature and Art



This is the golden ratio, or part of it at least. Commonly believed in art to be a very aesthetically pleasing proportion, it has a close relationship with the Fibonacci sequence.

From the fibonacci sequence, it can be calculated by taking the limit of the ratio of consecutive Fibonacci numbers (i.e. lim{n -> inf} [(F_n+1)/(F_n)])

Examples of the Fibonacci sequence can also be seen in a lot of different forms of nature.

Image result for romanesco broccoli
On a Romanesco broccoli, the number of spirals on a head is a Fibonacci number.
Image result for pine cone fibonacci spiral
The number of spirals going in each direction on a pine cone are also Fibonacci numbers!
Image result for flowers mixed
The number of petals on flowers usually correspond with Fibonacci numbers (e.g. 3, 5, 8, etc).

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