Rich with Fibonacci Gold

Let’s put this on the table before this conversation goes too far: I am not a fan of Math. I am a right-brained thinker, and math has always been and will always be my worst, absolute worst subject. By far.

However, sometimes mathematical concepts appear in Nature and in Art, so I take them on… one at a time. At least this one involves snails and rabbits.

FIBONACCI: A Simple Summary

The Place: Pisa, Italy
The Year: 1202
The Person: Leonardo Pisano Bigollo (who somehow became known as Fibonacci. Don’t ask me how.)

He pondered a simple brain-teaser about rabbits: “If a pair of rabbits is placed in an enclosed area, how many rabbits will be born there if we assume that every month a pair of rabbits produces another pair, and that rabbits begins to bear young two months after their birth?”

Fibonacci rabbits

A pattern emerges: the next number in the sequence is the sum of the two numbers before it.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …
 

How Fibonacci Turns to Gold

Now, from this little sequence we discover THE GOLDEN RATIO. If you divide one number in the sequence by the number before it, your answer will be approximately 1.618

ratio of fibonacci numbersThere is more gold to be had here. A rectangle that has sides equal to the Golden Ratio is called a GOLDEN RECTANGLE. You can keep dividing the smallest division of the rectangle by 1.618…

 FibonacciBlocks

This Golden Rectangle is the architecture for the Fibonacci Spiral (a.k.a. THE GOLDEN SPIRAL). This particular shape will retain its shape no matter the scale. It is equiangular: the radial line from the middle always makes the same angle to the curve.

Then, there’s the GOLDEN TRIANGLE, as follows.

Au Natural

Mother Nature hides Fibonacci numbers all over the place! The core florets on a daisy, sunflowers, pine cones, leaves on a pear tree, pineapples, etc. A snail shell is a classic example of the Fibonacci Spiral: as the snail outgrows a chamber in its shell, it builds a new one in the center, always in the same shape.

Leonardo Da Vinci in particular employed the Golden Ratio when studying anatomical proportions (his journals give us ample evidence of that). For example, you can detect the ratio in a face:

-Length of the face / distance between the tip of the jaw and where the eyebrows meet
-Length of mouth / width of nose
-Width of nose / distance between nostrils
-Distance between pupils / distance between eyebrows.

And the ratio doesn’t stop there! In 1985 and 1987, an American doctor and physicist revealed that the Golden Ratio is even in the structure of the human lung. “One feature of the network of the bronchi that constitutes the lung is that it is asymmetric. For example, the windpipe divides into two main bronchi, one long (the left) and the other short (the right). This asymmetrical division continues into the subsequent subdivisions of the bronchi. It was determined that in all these divisions the proportion of the short bronchus to the long was always 1/1.618.” 3

An Ingredient For Beauty and Art

In 2009, Adrian Bejan, a professor of mechanical engineering at Duke University, claimed that the human eye interprets images with the Golden Ratio faster than any other. For some reason, the ratio’s proportions are transferred to the brain more quickly from any other: “Shapes that resemble the golden ratio facilitate the scanning of images and their transmission through vision organs to the brain. Animals are wired to feel better and better when they are helped and so they feel pleasure when they find food or shelter of a mate. When we see proportions in the golden ratio, we are helped. We feel pleasure and we call it beauty.”2

So, does the Fibonacci Sequence play a key role in Beauty? Well, that discussion will have its very own post, I assure you.

As for Fibonacci’s (and Math’s) grander role in Art, I leave you with this quote:

“In art the control of reason means the rule of design. Without reason art becomes chaotic. Instinct and feeling must be directed by knowledge and judgment. It is impossible to correlate our artistic efforts with the phenomena of life without knowledge of life’s processes…[the artist] can direct his artistic fate only by learning nature’s ideal and going directly for that as a goal.”1

Sources
1. Hambidge, Jay. The Elements of Dynamic Symmetry. Dover Publicantions, Inc. New York: 1967.

2. McVeigh, Karen. “Why golden ratio pleases the eye: US academic says he knows art secret.” Guardian, December 28, 2009. guardian.co.uk (accessed May 9, 2013).

3. Yaha, Harun. “Fibonacci Numbers: A Measure of Beauty”. Islamic Research Foundation International, Inc. http://www.irfi.org/articles/articles_251_300/fibonacci_numbers.htm (accessed May 9, 2013).

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