The Brunardot Series.

[Epsilon=One]

The Brunardot Series (BS)

The Brunardot Series is a simple, additive series of unending sequences, each with simple, additive, unending terms, such that: when the first term is "x" the second term is the Natural function (www.101123.com/NF), "x² – x."

Thus the Brunardot Series is:

http://i.g2d.us/bsc500.gif

It is the Brunardot Series that unifies all phenomena. It is born of complex oscillations of vibration, slide, and swing.

Even Pi, Phi, Circles, Ellipses, Sinusoidal curves, and the revised Fibonacci Sequence (www.101123.com) (rFS) are directly related. Something that Einstein would love; as, he sought to relate the sinusoidal equations of Light (special relativity) with the elliptical equations of Gravity (general relativity).

If the first term is One, "1," both a circle and the revised Fibonacci sequence (www.101123.com) (rFS) is generated.

If the second term is One, "1," the first term is the Golden Ratio (www.101123.com/GR).

If the first term, or third term, is Two, "2," an ellipse is generated that yields the Natural integers (www.101123.com/NI): 1, 2, 3, 4, 5, 6, 7, 8, for its most salient structural parts (www.101123.com/SSP) (SSP).

(If no image appears below, "Click" your browser "Refresh" icon.)
Integer
http://i.g2d.us/bs.gif
Any ellipse generated by any sequence of the Brunardot Series establishes The Inverse Square Law (www.101123.com/ISL) and orthogonal dimensions.

The Brunardot Series demonstrates the uniform distribution of the Natural prime numbers (www.101123.com/NPN) . . . Nature's Units. That is; said primes, that are the value of certain focal radii, can be mapped with a simple algebraic function to the perigee of its respective Brunardot Ellipse (www.101123.com/BE) that is generated from the sequences of said series.

And for any ellipse so generated, when the perigee (www.101123.com/Parts), "p," is an integer, so is the hypotenuse (http://www.physicsmathforums.com/showthread.php?t=106) . . . and the apogee ( www.101123.com/Parts), and the radius ( www.101123.com/Parts), and the soliton ( www.101123.com/Parts), and the vector ( www.101123.com/Parts), and the wave ( www.101123.com/Parts), and the glyph ( www.101123.com/Parts), and the major diameter ( www.101123.com/Parts). Also, as is often, and predictably, the amplitude ( www.101123.com/Parts), diameter chord ( www.101123.com/Parts), and diagonal radial ( www.101123.com/Parts).

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[ed van der meulen]

I think I can understand you.

My question is why is the Brunardot Series showing this? Could you explain that to me. I understand that it works. But what is the secret behind it?

And a very nice topic. I am a pure mathematician as well. Trying to unite all people with brains. But we have to listen to others for that.

Have a nice day

ed

[Epsilon=One]

My question is why is the Brunardot Series showing this? Could you explain that to me. I understand that it works. But what is the secret behind it?The Brunardot Series is generated by the intrinsic geometry of seminal motion (http://www.physicsmathforums.com/showthread.php?t=179) as heuristically described by Brunardot Ellipses (http://www.physicsmathforums.com/showthread.php?t=104). Did you notice that the Brunardot Series revises the Fibonacci sequence (http://www.physicsmathforums.com/showthread.php?t=103) after some 750 years?

And a very nice topic. I am a pure mathematician as well. Trying to unite all people with brainsA worthy goal. The brains are not difficult to find. An open mind is quite another thing.

[ste]

Even Pi, Phi, Circles, Ellipses, Sinusoidal curves, and the revised Fibonacci Sequence (rFS) are directly related. Something that Einstein would love; as, he sought to relate the sinusoidal equations of Light with the elliptical equations of Gravity.


Could you provide further illustration of how Phi, pi, and rFS are unified by the Brunardot series?

[Epsilon=One]

Could you provide further illustration of how Phi, pi, and rFS are unified by the Brunardot series?The answer to your query seems clear (though, apparently not) as I succinctly described the Brunardot Series in Post #1, above.

Can you be more specific as to what particular words that you do not understand?

The Natural source of the Brunardot Series (BS) is a Pulsoid (http://www.CQthus.com/PT/P).

Any integer sequence of the Brunardot Series generates a Brunardot Ellipse (http://www.CQthus.com/PT/BE) (BE).

[ste]

My appologies. Looks like my browser didn't load the appropriate image relating phi to the rFS.

[Epsilon=One]

My appologies. Looks like my browser didn't load the appropriate image relating phi to the rFS.Accepted. Now, I understand; you had me confused.

I love your signature!!!

[ste]

I am intrigued by this quixotic "sphere of reality". What is this sphere? How does it relate to Reality? Why are natural prime numbers inexorably linked with nature? I thought that a circle with a radius of 1 was the radius of Infinity, not Reality.

Why does the Fibonacci Sequence need revision?

Why do you group numbers in one of your diagrams into three categories (Infinity, Reality, and Universe), if Reality and Universe are essentially the same thing?

I've also noticed the 'radius' (AD=BJ) in an ellipse and wondered what it represents.

A connection between phi and the Fibonacci numbers can also easily be seen in that:

Fibonacci numbers: F(n+2)-F(n+1)-F(n)=0
Golden Ratio: x^2-x-1=0

[Epsilon=One]

I am intrigued by this quixotic "sphere of reality"I don’t refer to the “sphere of reality” as quixotic.

What is this sphere? How does it relate to Reality?It is intended to connote Reality (www.CQthus.com/PT/R).

Why are natural prime numbers inexorably linked with nature?Succinctly: because Nature generates all integers; or arguably, vice versa.

More precisely: Natural prime numbers are found within the geometric constructs of Nature.

I thought that a circle with a radius of 1 was the radius of Infinity, not Reality.The Elliptical Constant (www.CQthus.com/PT/EC) (EC) does heuristically represents the radius of Infinity (www.CQthus.com/PT/ROI) (ROI). And, ROI is congruent with the locus of Reality . . . at all points within Reality.

Why does the Fibonacci Sequence need revision?Because the Fibonacci sequence (FS) is incomplete and a subset of a more general series. There is little Natural logic to the choice of its first and second terms; in fact, its first two terms are debatable as to whether they are: 0, 1 or 1,1.

Because the FS is so closely related to Nature; and, that relationship is ubiquitous and inexplicable, it is only logical to find a Natural origin which happens to be the geometry of the ellipse and a generalized unending series related to the ellipse, to which it belongs.

Such a series is the Brunardot Series (BS) which has its first sequence as the revised Fibonacci sequence (www.CQthus.com/PT/rFS) (rFS) that begins: 1, 0 as opposed to the unrevised beginnings of either 0,1 or 1,1 that are without any compelling Natural reason.

I find it amazing with all the Fibonacci magazines, clubs, etc. that no one has picked up on the rFS for the 10 or fifteen years its been on the internet. Of course, little amazes me when I consider the "ignore"-ance (www.CQthus.com/PT/Ignore) of academic mathematicians and theoretical physicists anymore.

Why do you group numbers in one of your diagrams into three categories (Infinity, Reality, and Universe), if Reality and Universe are essentially the same thing?Because the second term of each sequence so designated is Zero, “0.” Which signifies a singularity which describes the congruent loci of Infinity and Reality. The integers of all the other sequence exist and are, thus, part of the Universe.

I've also noticed the 'radius' (AD=BJ) in an ellipse and wondered what it represents.I don’t understand the relevance to this thread; however, the radius, “r,” and the hypotenuse, “h,” equals two vectors, “2v”; and thus, their intersection is on the elliptical locus and they are orthogonal with the major diameter; and, they are harmonic integers when the Pulse is an integer. The radius is so named because it is a radius of a perpendicular section at a focus of an ellipsoid that rotates about its major diameter, “M.”

A connection between phi and the Fibonacci numbers can also easily be seen in that:

Fibonacci numbers: F(n+2)-F(n+1)-F(n)=0I don’t understand. “F(n+2)-F(n+1)-F(n)” equals F(1–n) not 0.

Golden Ratio: x^2-x-1=0 I don’t understand. The Golden Ratio (www.CQthus.com/PT/GR) (GR) equals (√5 – 1)/2.

Incidentally, the usual connection between the FS and the GR is the convergence of consecutive terms. This is not a good connection; as any additive sequence so converges. The best connection between the FS and the GR is the geometry of the ellipse; and, such geometry is the geometry of the Brunardot series (BS) with its first sequence the revised FS: 1, 0, 1, 1, 2, 3, 5…

[ste]

If the first term is One, "1," both a circle and the revised Fibonacci sequence (rFS) is generated.

It is apparent how the revised Fibonacci Sequence is derived from the Brunardot Series. However, I fail to see how a circle is generated. Please explain?

[Epsilon=One]

It is apparent how the revised Fibonacci Sequence is derived from the Brunardot Series. However, I fail to see how a circle is generated. Please explain?When the first term is 1, the third term is 1² = 1, the second term, the Natural function, is 1 – 1 = 0, the fourth term is 0 + 1 = 1.

Thus, 1, 0, 1, 1... the first integer sequence of the Brunardot Series (BS) and the . . . revised Fibonacci sequence (www.CQthus.com/PT/rFS) (rFS).

All ellipses are constructed from a Brunardot Series sequence with the first term the perigee, the second term the Natural function (www.CQthus.com/PT/NF) (soliton), the third term the vector, and the fourth term the apogee.

An ellipse with the perigee, vector and apogee = 1 and the Natural function = 0 describes a circle.

An ellipsoid quantum with a vector = 0 is a sphere without a pulse (motion); thus the spherical quantum (as used in most all physical field calculations) does not exist. Quanta are spheroidal not spherical (spherical as per MDT theory, etc.).

Or, stated in another manner, the radius of an ellipsoid (sphere) with a perigee of 1 = r = 2p – 1 = 1; therefore, a quantum sphere with a radius of 1 does not exist (vector and soliton = 0); thus, it can be stated that the radius of Infinity is Gödel (www.CQthus.com/PT/Go)’s long sought “One.” Ipso (www.CQthus.com/PT/IPSO) facto.