Math in Nature and Art

on

1.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137484754088075386891752126633862223536931793180060766726354433389086595939582905638322661319928…

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).

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s