Wednesday, May 8, 2013

Happy Fibonacci Day!

Today is Wednesday, May 8, 2013.

It's not really "Fibonacci Day," but the numbers 5, 8, and 13 are next to each other in the Fibonacci sequence.

What is the Fibonacci sequence?  If you start with the numbers 0 and 1, then add them together, the sum is 1.  You keep on adding the two last numbers in the series to get the next number.  Therefore, the first few numbers in the series are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, on and on to infinity.  The sequence is named after Leonardo of Pisa, whose nickname, Fibonacci, means "son of Bonacci," since he was the first to introduce this concept to the western world.  Indian manuscripts written in Sanskrit noted this same sequence as early as the sixth century, but even the mathematicians of India didn't "invent" it.  God did, and the evidence is found everywhere in nature.

As you can see, a Fibonacci Day can only occur on a day in which the date is written in digital form, with only the last two digits of the year.  The the next Fibonacci Day will be on August 13, 2021.  After that there won't be any more Fibonacci Days until May 8, 2113.  The last two Fibonacci Days were May 8, 1913 and August 13, 1921, but, of course, people were not in the habit of writing the date digitally, so no one seemed to notice.  

The Fibonacci arc depicted in the illustration above can drawn with an ordinary compass like the one shown at right.  With the compass, you can draw circular arcs that connect opposite corners of larger and larger squares.  The resulting shape can be found all over the place.

The Fibonacci sequence can be used to describe the results of mating rabbits and bees, for example.  It can also be used to describe the pattern of branching in trees, the way leaves are arranged on a plant stem, the flowering of an artichoke, and the arrangement of scales on any pine cone you care to pick up and examine.  Many flowers have a spiraling sequence of petals that follow the Fibonacci order.

The spiral shape is found in the uncurling of new fern leaves, a nautilus shell, or the way a caterpillar curls up before forming a cocoon.  It is also found in weather patterns.  One blogger was even able to show patterns of population density in Africa using a Fibonacci spiral.  Many galaxies are arranged in spirals, as well, including our own Milky Way Galaxy.  Even the ovaries of an Angelfish display a Fibonacci spiral.  The proportions of many animals follow Fibonacci patterns, including the proportion of bones in your fingers and the ratio of forearm length to the length of your hand.  The cochlea of your inner ear is also in the shape of a "Golden Spiral," and your fingerprints are arranged according to the Fibonacci sequence, as well.

Since a picture is worth a thousand words, here are some amazing photographs of what I've been talking about.  :-)

Roman cauliflower
Angelfish ovary
snails and human fingerprints
nautilus shell
pine cone

aloe leaves
leaves of many plants, looking from the top

branching in trees and other plants

oval shape of an egg

scales on a pineapple
Monarch caterpillar

hurricane spiral
spiral galaxy as seen by Hubble telescope

pattern of population density in Africa
Fibonacci curve as shown in The Wave, by Hokusai

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