
THE FIBONACCI SEQUENCE

JUNE 1, 2017



Greetings Dear Friends
May is my favorite month  Mother Nature all decked out in greens and blossoms of all colors. The other day I overheard some people talking about the Fibonacci Sequence, a series of numbers that represents one of nature's more amazing phenomena. I noticed that these people had an incomplete understanding of the whole thing, something I've experienced several times in the past. It inspired me to present this wee article about the Golden Mean and the Fibonacci Sequence.
The next meeting of the TrumpEra Discussion Group will happen on Sunday, June 4th. If you are interested in joining the group, send me a message by replying to this email.
Also, there is an important event happening in Erin on June 11. See details below.
If you'd like to access past newsletters containing articles on the Big Shift, the Physics of Mysticism, Magic, the Power of Mantra, Conciousness and other topics, please visit the 'newsletter' page of my website: whyislife.com


THE FIBONACCI SEQUENCE
by Dennis Gaumond
In order to understand the Fibonacci Sequence, it is necessary to understand the geometrical phenomenon on which it is based. The Golden Mean, the Golden Section, the Divine Proportion these are names given to a very special ratio that appears in countless contexts throughout nature. This ratio is represented mathematically as 1:1.618033988749895... and this number is called 'phi' (not to be confused with 'pi'). Phi is represented by this Greek symbol  Φ. Say we had three lines of increasing length, Lines A, B and C. If Line B was 1.618 times as long as Line A and Line C was 1.618 times as long as line B, then these lengths would conform to the phi ratio. Conversely, with diminishing lengths, B would be .618 times the length of C and A .618 times the length of B. With this special ratio, the combined length of Lines A and B would equal the length of C.
This ratio can be derived in several ways including mathematically and geometrically. Its most well known derivation comes from something called the Golden Rectangle. In this case the length of the rectangle would be 1.618 times the width. If one had such a rectangle and severed a perfect square from it, one would be left with a rectangle that had the same phi proportions as the original rectangle.
Phi is known as the Divine Proportion because so many patterns in nature conform to it. For example, the bones of a human hand, from fingertip to wrist, increase in size according to this ratio. Also, the length from wrist to elbow is roughly 1.618 times bigger than from fingertip to wrist. (I say 'roughly' because the phi ratio is an ideal, an archetype, and in nature there is always slight variation.) These proportions can be seen in many body parts, including both the front view and profile of a human face. It also applies to the proportions in other animals, growth patterns in plants, heartbeat patterns, seashell spirals and much more. It can even be seen in the DNA molecule, the program for all life. The length of a full cycle of its double helix spiral is 1.618 times greater than its width. Phi can be seen in the distances between planets in our solar system, in the patterns of population growth of many species, the frequencies in the color spectrum and in many musical relationships. The distance between frets on a guitar decreases according to this ratio as one moves up the neck.
Interestingly, humanity has known about this special ratio for thousands of years. It has been used throughout history as an aesthetic standard in art. It is represented in the layout of many great paintings and in the proportions of many works of architecture, such as the Great Pyramid, the Parthenon, the Cathedral of Notre Dame and recently, in the United Nations building. Phi can be found in the Bible. God's instructions to Moses for the building of the Ark of the Covenant (Exodus 25:10) contain strict proportions of width to length, which conform to this ratio. Phi can be seen in God's instructions to Noah regarding the proportions of the ark that he is to build. (Genesis 6:15)
One of the difficult aspects of understanding the Divine proportion is that, in its pure, ideal mathematical form, it is a sequence that increases by 1.618 into macro infinity, and decreases by .618 into micro infinity. It has no beginning and no end. But, of course, as we see it manifesting in physical form, it does have a beginning. In the 12th century, a mathematician named Leonardo Fibonacci discovered a number sequence that, as closely as possible, represents the phi phenomenon. It starts with 0 and 1, and each new number in the series is the sum of the previous two numbers, i.e. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. The further along in the series, the closer the ratio between adjacent numbers approximates the phi ratio. For example, 5 divided by 3 is 1.666..., 8 divided by 5 is 1.60 and 144 divided by 89 is 1.6179...
The Fibonacci Sequence and its offspring, the Fibonacci Spiral, can give us great insight as we continue to unravel the great mysteries of life. For more info, an Internet search will yield countless entries, such as http://www.goldenmeanspiral.com

WATERSTOCK  JUNE 11
This is a great event organized by the Wellington Water Watchers. Do you feel strongly, as I do, that water belongs to all of us and that we shouldn't have to buy it from big corporations? If so, come out to support this initiative. It promises to be a great way to spend a Sunday afternoon with great music and speakers.

'WHY IS LIFE?' NOW ONLY $6
My book, Why Is Life?, has been released as an ebook, available for approximately $6 or less, from a list of online bookstores:
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