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Postulate, Corollaries, and Theorems A statement of First Cause.

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Old 02-11-2008, 11:42 PM
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Epsilon=One Epsilon=One is offline
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Default The revised Fibonacci Sequence (rFS)

The revised Fibonacci Sequence (rFS)
1, 0, 1, 1, 2, 3, 5...


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This post is in memoriam: Leonardo Fibonacci
[ca. 1175-ca. 1250]

The revised Fibonacci Sequence is the first Natural integer sequence of the Brunardot Series (BS).
(Note: the coefficients of the Brunardot Series (BS) terms are Fibonacci numbers.)

The Brunardot Series (BS) is:


Thus, the revised Fibonacci Sequence is:

1, 0, 1, 1, 2, 3, 5... .......

Fibonacci probably began the sequence with 1 and 1 as the first two terms; as, zero was little used or accepted as an integer in his day. Yet, many sources cite 0 and 1 as the first two terms. There are no known sources that cite 1 and 0 as the first two terms of the sequence, which are the most logical beginning terms; as, they arise from the first Natural integer values of the Brunardot Series (BS) that is found in the seminal motion of all fundamental phenomena, which explains the ubiquity of the Fibonacci Sequence in Nature.

Both the revised Fibonacci Sequence (rFS) and the Golden Ratio (GR) are firmly established at the first instance of Triquametric motion.

The revised Fibonacci Sequence begins with the first Natural integer and is generated by the second term that is the Natural function of the first term that in the Pulsoid is referred to as the soliton, "s."

It is, also, the Brunardot Series (BS) relationship with the Brunardot Ellipse (BE) that accounts for the revised Fibonacci Sequence’s direct association with the Elliptical Constant, Golden Ratio, Phi and the circular constant, pi. (The circle is an ellipse with the perigee, "p," and the radius, "r," equal to One, which is the Elliptical Constant (EC), r = 2p – ε. The soliton, “s,” does not exist when the ellipse is a circle, s = p² – p. Which is one explaination of why a sphere with the radius of “ε” represents the non-existence of Infinity.)


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Old 02-29-2008, 10:01 PM
Midgar21 Midgar21 is offline
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Default So what is the significance?

If understand correctly, you see the revision for the Fibonacci sequence for this reason:

...when e=1 and the key, "k," equals 1, the values of the salient structures of an ellipse which you have defined (wave, soliton, apogee, perigee, hypotenuse, glyph, etc...) can be arranged to form the Fibonacci sequence.

To skeptics, this would seem to be seriously contrived: the rest of the elliptical structures can be arranged to match the integers of the Fibonacci sequence except for epsilon, which is why you have added "1" to the beginning. Mathematically, this works out, but only because you have arranged the structural components to be in accordance with the Fibonacci sequence and added that "1."

What exactly is the function/significance of the relationship between the Fibonacci sequence and your structural components of a Brunardot Ellipse? If one is to make the claim that the Fibonacci sequence is to be revised, there should be some reason as to why it should.
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Old 11-23-2008, 07:48 AM
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Epsilon=One Epsilon=One is offline
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Default The revised Fibonacci sequence is the first sequence of the Brunardot Series.

Quote:
Originally Posted by Midgar21
If understand correctly, you see the revision for the Fibonacci sequence for this reason:

...when e=1 and the key, "k," equals 1, the values of the salient structures of an ellipse which you have defined (wave, soliton, apogee, perigee, hypotenuse, glyph, etc...) can be arranged to form the Fibonacci sequence.
Not exactly. I see all ellipses to have salient features that reflect the Brunardot Series (BS). I see the first integer sequence of this series as: 1, 0, 1, 1, 2, 3, 5….. It is this first sequence that I refer to as the revised Fibonacci sequence (rFs). And, as ellipsoids are the major structure of all micro/macro motion . . . and quanta . . . this explains why the incomplete, common portion of the revised Fibonacci sequence (rFs) is ubiquitous in Nature.

Quote:
Originally Posted by Midgar21
To skeptics, this would seem to be seriously contrived: the rest of the elliptical structures can be arranged to match the integers of the Fibonacci sequence except for epsilon, which is why you have added "1" to the beginning.
This just is not so. One was not contrived nor “added”; nor, is the Elliptical Constant symbolic of the first integer of said sequence; One is the first integer sequence of said Brunardot Series.

Quote:
Originally Posted by Midgar21
Mathematically, this works out, but only because you have arranged the structural components to be in accordance with the Fibonacci sequence and added that "1."
I can find no evidence for this argument.

Quote:
Originally Posted by Midgar21
What exactly is the function/significance of the relationship between the Fibonacci sequence and your structural components of a Brunardot Ellipse? If one is to make the claim that the Fibonacci sequence is to be revised, there should be some reason as to why it should.
The Fibonacci sequence as currently presented by the mathematics community ( beginning with “0, 1” or “1,1”) has no geometric rationale for its beginning . . . nor has the number system, itself, any such rationale. See above first reply for the rationale for a “1,0” beginning..
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