The Fibonacci Spiral
Thou art worthy, O Lord, to receive glory
and honour and power: for thou hast created all things, and for thy
pleasure they are and were created.
The 12th century Monk Leonardo Pisano Bigollo, better known as Fibonacci, is best known to the modern world for the spreading of the Hindu–Arabic numeral system in Europe and for graphically interpreting the Fibonacci Sequence as the Fibonacci Spiral.
Spirals in Nature:
The Fibonacci series appears in the foundation of aspects of art, beauty and life. Also known as Phi and The Golden Ratio, it is a fascinating numerical property embedded within God's creation; a blueprint, or algorithm so to speak, in which a blueprint speaks of and points back to its creator. The Fibonacci Sequence is the series of numbers:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987,… The next number is found by adding up the two numbers before it.
The 2 is found by adding the two numbers previous (1+1). Similarly, the 3 is found by adding the two numbers before it (1+2), the 5 is (2+3) and so on.
Fibonacci numbers are of interest to biologists and physicists because they are frequently observed in various natural objects and phenomena. The branching patterns in trees and leaves, for example, and the distribution of seeds in a raspberry are based on Fibonacci numbers.
The Fibonacci numbers occur repeatedly in the petal arrangement of flowers. Examine the crisscrossing spiral seed pattern in the head of a sunflower, for instance, and you will discover that the number of spirals in each direction are invariably two consecutive Fibonacci numbers.
The growth of a nautilus shell, like the growth of populations and many other kinds of natural “growing,” are somehow governed by mathematical properties exhibited in the Fibonacci sequence. And not just the rate of growth, but the pattern of growth.
The human body: Take a good look at yourself in the mirror. You'll notice that most of your body parts follow the numbers one, two, three and five. You have one nose, two eyes, three segments to each limb and five fingers on each hand. The proportions and measurements of the human body can also be divided up in terms of the golden ratio. DNA molecules follow this sequence, measuring 34 angstroms long and 21 angstroms wide for each full cycle of the double helix
If you use your fingernail length as a unit of measure, the bone in the tip of your finger should be about 2 fingernails, followed by the mid portion at 3 fingernails, followed by the base at about 5 fingernails. The final bone goes all the way to about the middle of your palm, which is a length of about 8 fingernails. Again, it's Fibonacci at work and the ratio of each bone to the next comes very close to the golden ratio.
Musical scales are based on Fibonacci numbers. In music, the basic structure of a piano keyboard consists of an octave of thirteen notes, eight of which are white and five of which are black. The black keys come in groups of two and three:
• There are 13 notes in the span of any note through its octave.
• A scale is composed of 8 notes, of which the
• 5th and 3rd notes create the basic foundation of all chords, and
• are based on whole tone which is 2 steps from the root tone, that is the 1st note of the scale.
Note too, how the piano keyboard scale of C to C above of 13 keys has 8 white keys and 5 black keys, split into groups of 3 and 2. While some might “note” that there are only 12 “notes” in the scale, if you don’t have a root and octave, a start and an end, you have no means of calculating the gradations in between, so this 13th note as the octave is essential to computing the frequencies of the other notes. The word “octave” comes from the Latin word for 8, referring to the eight whole tones of the complete musical scale, which in the key of C are C-D-E-F-G-A-B-C.
In a scale, the dominant note is the 5th note of the major scale, which is also the 8th note of all 13 notes that comprise the octave. This provides an added instance of Fibonacci numbers in key musical relationships. Interestingly, 8/13 is .61538, which approximates phi. What’s more, the typical three chord song in the key of A is made up of A, its Fibonacci & phi partner E, and D, to which A bears the same relationship as E does to A. This is analogous to the “A is to B as B is to C” basis for the golden section, or in this case “D is to A as A is to E.”
"In the beginning there was nothing, and then it exploded." -Chuck Missler
Random chance resulting in cosmos via a large primordial explosion from the point of singularity, or an exquisitely organized mathematical sequence designed to declare the presence of the Creator to those who look for Him?