Fibonacci... (son of Bonacci), Leonardo Bonacci was the son of Guglielmo Bonaccio of Pisa and an Italian mathematician from the Republic, considered to be "the most talented Western mathematician of the Middle Ages." His study of what became known as "The Fibonacci Numbers" followed similar studies by others from many countries of an older world, and contributed to understanding the "Golden Mean" or "Golden Rectangle" used in many instances of painting and architecture throughout history as well as documenting myriad occurrences in nature.
The natural spiral in sunflowers and shells of many sea creatures is described referencing a rectangle of very specific proportions and characteristics. To establish the ratio diagrammatically this rectangle has a short side with the dimension of (1) and a long dimension of (1.6180). Strangely if you make a square within the overall rectangle (1:1.6180), the square having all sides of (1), the smaller rectangle that remains is in the exact proportion as the original 1:1.6180 rectangle. When several of these cycles have been repeated and the centers of the squares connected by a curved line, the spiral created is the same as the spiral in the positions of Sunflower Seeds in a blossom or the form of the Chambered Nautilus and thousands of other instances in nature.
My simple use of this phenomenon is applying the ratio of 1:1.6180 to the placement of photographs on paper and, in certain instances, the shape of the paper; the space above the image is in this proportion to the space below and the photographic paper is trimmed to that same ratio when the image is square. Is this presentation of white space and paper shape conducive to a better viewing experience? Over time I might come to feel more comfortable with the principle applied this way. Knowing that commercial paper shapes and sizes are directly tied to newspaper column width and shape abrogates my allegiance to those shapes to some degree.
(This is hardly an explanation of Fibonnaci's discoveries or applications and observances. An interested student of natural phenomena can find extensive resources at will.)