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

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Old 02-12-2008, 12:42 AM
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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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Last edited by Epsilon=One; 07-29-2015 at 04:15 PM. Reason: Format
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