Fibonacci is Everywhere

A golden rectangle (in pink) with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a.

From https://en.wikipedia.org/wiki/Golden_ratio

Fibonacci is everywhere…

In Nature:

Video: https://www.youtube.com/watch?v=LfX9AVivyzw

Image: http://www.shiftfrequency.com/fibonacci-sequence-in-nature/

Image: http://tamrajhiggins.com/?cat=82

Image: http://tamrajhiggins.com/?cat=82

Some interesting information about shells and the relationship to the golden ration can be found here: https://www.goldennumber.net/nautilus-spiral-golden-ratio/

 

In Art:

Images and Text: https://yabm.wordpress.com/2010/05/15/phi/

Mona Lisa’s head fits perfectly inside a golden rectangle, and the distance from the bottom of her face to her eyes is in a golden ratio with that from her eyes to the top of her face.  And this is not just artistic license.  To some degree almost every dimension of our faces can be seen to conform in some way to the golden ratio,  even down to the shape of our teeth (our two front incisors approximate a golden rectangle, and the ratio of one front incisor to the next smallest tooth is roughly  It has even been suggested that a person’s perceived attractiveness is partly dependent on how close certain measurements of their facial features are to golden ratios.

Golden ratios abound in da Vinci’s famous “Vitruvian Man”, for example.  These range from golden rectangles that have actually been partially explicitly drawn in – such as that comprising the figure’s torso – to more hidden appearances.  The circle in the drawing takes as its radius the length which forms a golden ratio with the side of the square.  And the length from the bottom of the figure’s feet to its navel is in a golden ratio with that from the navel to the top of the head.

  

 

In Architecture:

Many of the ancient Greek buildings, like the Parthenon, had golden rectangles. The National Gallery in London, England also had golden rectangles. There are many other famous buildings that have golden rectangles in them

(Text: https://prezi.com/sxhuc0ytm36b/fibonacci-in-architecture/)

Image: https://www.youtube.com/watch?v=L8PSp8rKVXQ   

Image: https://www.flickr.com/photos/tjblackwell/8313250246