I have long been fascinated by the phenomena of phi (Greek letter), the Fibonacci number series, and the Divine proportion, Golden Proportion, Golden mean, Golden ratio, Golden spiral, Golden rectangle. To me this is such a clear evidence of God’s existence and His mighty genius in the creation of all things in nature. If you’ve never heard of this, look into it – you will be amazed! But here are some facts and examples to get you started.
In mathematics, the Fibonacci series are the numbers in the following sequence of integers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. where the first two numbers are 0 and 1, and each subsequent number = the sum of the previous 2 numbers.
And Phi = 1.6180339887… or the ratio of any Fibonacci number to the previous number in the sequence, e.g. 8/5, 13/8, etc.
The Fibonacci series is named after Leonardo of Pisa, who introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian mathematics. Fibonacci numbers are used in the analysis of financial markets. They also appear in biological settings, such as branching in trees, arrangement of leaves on a stem , the fruit spouts of a pineapple , the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone.
You can see this divine proportion of beauty in every aspect of creation, from botany to zoology, to the human body, the human face in particular, in the color spectrum, in musical scales and chords, in astronomy, in architecture, even in the patterns of our DNA! and especially for this post, in God’s instructions to the Jews in building such articles as the holy Ark of the Covenant, Noah’s Ark, the color arrangements in the Jewish Tabernacle in Exodus. God evidently designed the universe with this ratio as the basis of its appearance, from the microcosm to the macrocosm. Here are just a few examples of this phenomenon.
Some plants have beautiful repeating spiral patterns to their structures that incorporate the so-called golden angle (approx 137.5 degrees). Math buffs, artists, and mystics will appreciate that the golden angle is related to the “divine proportion” that frequently appears in aesthetically-pleasing forms.
Plants with spiral patterns related to the golden angle also display another curious mathematical property. The seeds of a flower head form interlocking spirals in both clockwise and counterclockwise directions. The number of clockwise spirals differs from the number of counterclockwise spirals, and these two numbers are called the plant’s parastichy numbers (pronounced pi-RAS-tik-ee or PEHR-us-tik-ee). These numbers have a remarkable consistency. They are almost always two consecutive Fibonacci numbers.
Phi in the Bible and Creation
Although perhaps not immediately obvious, phi and the golden ratio appear in the Bible.
In Exodus 25:10, God commands Moses to build the Ark of the Covenant, in which to hold His Covenant with the Israelites, the Ten Commandments, saying, “Have them make a chest of acacia wood- two and a half cubits long, a cubit and a half wide, and a cubit and a half high.” The ratio of 2.5 to 1.5 is 1.666…, which is as close to phi (1.618 …) as you can come with such simple numbers and is certainly not visibly different to the eye. The Ark of the Covenant is thus constructed using the Golden Section, or Divine Proportion. This ratio is also the same as 5 to 3, numbers from the Fibonacci series.
In Exodus 27:1-2, we find that the altar God commands Moses to build is based on a variation of the same 5 by 3 theme: “Build an altar of acacia wood, three cubits high; it is to be square, five cubits long and five cubits wide.”
Note: A cubit is the measure of the forearm below the elbow.
In Genesis 6:15, God commands Noah to build an ark saying, “And this is the fashion which thou shalt make it of: The length of the ark shall be three hundred cubits, the breadth of it fifty cubits, and the height of it thirty cubits.” Thus the end of the ark, at 50 by 30 cubits, is also in the ratio of 5 to 3, or 1.666…, again a close approximation of phi not visibly different to the naked eye. Noah’s ark was built in the same proportion as ten arks of the covenant placed side by side.
The colors of the Tabernacle are based on a phi relationship
As it says in Exodus 26:1, “Make the tabernacle with ten curtains of finely twisted linen and blue, purple and scarlet yarn, with cherubim worked into them by a skilled craftsman.” This reference to the combination blue, purple and scarlet in the construction of the tabernacle appears 24 times in Exodus 25 through 39, describing the colors to be used in the curtains, waistbands, breastpieces, sashes and garments.
Phi relationships in a color spectrum produce rich, appealing color combinations
Michael Semprevivo has introduced a concept called the PhiBar, which applies phi relationships to frequencies, or wavelengths, in the spectrum of visible colors in light. Colors in the spectrum that are related by distances based on phi or the golden section produce very rich and visually appealing combinations. This is illustrated below on the screen shot of his PhiBar program. You can experiment with the PhiBar program, written in Visual Basic, by clicking HERE to download it and then running the .exe file.
Note: This program is made available by Michael Semprevivo for free for non-commercial use only. The PhiBar.exe program was scanned with Norton’s Antivirus program on 03/01/2003 using current virus definitions and found to be virus free but no express or implied warranties are given with respect to its use.
The PhiBar produces the color combinations of the Tabernacle as described in the Bible
Using the PhiBar program above, J.D. Ahmanson discovered that it produces the colors that the Bible says God gave to Moses for the construction of the Tabernacle.
The DNA spiral is a Golden Section
The DNA molecule, the program for all life, is based on the golden section. It measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. 34 and 21, of course, are numbers in the Fibonacci series and their ratio, 1.6190476 closely approximates phi, 1.6180339.
Musical scales are based on Fibonacci numbers
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. 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.”
Musical instruments are often based on phi.
Fibonacci numbers and phi are used in the design of violins and even in the design of high quality speaker wire.
Have you seen enough? Isn’t God awesome in his precise and beautiful engineering? And to think that some still believe it all happened by chance! I could go on but this post is getting long! Do look into it yourself and be more amazed! Much of this information is taken from this website: http://goldennumber.net/index.htm .