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

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Old 02-10-2008, 11:51 PM
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Epsilon=One Epsilon=One is offline
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Default The Elliptical Constant (EC)

The Elliptical Constant (EC)

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This post is in memoriam:
Euclid of Alexandria
[ca. 325 - ca. 265 B.C.E.]

There is a constant for ellipses, more so than "pi" is a constant for circles, such that the relationship of every structural part, for any ellipse to a similar structural part of any other ellipse, is always the same ratio as expressed by the same simple equation. This constant, often expressed as a difference or the radius of Infinity (ROI), is true for ellipses of any size . . . from smaller than a Planck quantum to larger than the orbits of galactic stars.

The Elliptical Constant (EC), εpsilon, “ε,” is, Naturally, directly related to Pi, “π.”

It is the EC, a heuristic definition of the Conceptual Unit (CU), that makes Pulsoid Theory "work." Seminal motion, Pure motion, is interrupted by the resultant harmony and resonance of seminal motion that is created when the CU is found among the chaos of hyper-relativistic motion of dynamic, emergent separation (DES) when a dimensionless point separates from a dimensionless sphere.

In accordance with the principles of Unimetry's Brunardot Theorem and Conceptual Ellipses, all salient structural values of any elliptical shape are Natural integers, which are multiples of the EC.

The Brunardot Theorem describes every ellipse; and, every elliptical shape is a Conceptual Ellipse when the EC, εpsilon, equals One.

Thus, it is the EC, as a common denominator that equals One, that fundamentally establishes the integers of all number systems. Thus, every number system is fundamentally derived from the ellipsoids of seminal motion as they are the fundamental basis of elliptic structures.

Thus, numbers because
they occur from the internal structure
of the ellipsoids of seminal motion
can be considered as analogous to
other dimension that so evolve;
such as the simultaneous occurrence of time;
which is preceded by the concepts of
orthogonality and the Inverse Square Law.

The discovery of the EC and its significance is a most important milestone in the history of mathematics.

It is the EC that reconciles, with one another: the spin of fermions and bosons; accelerating, galactic recession; and, Natural integers.

The Proof of One, which “One” is the Elliptical Constant, ε = One.

It is the EC that sets the “beat” of the metronome of Reality, which adds the “pulse” to Triquametric motion. It is this constant pulse that is the “clock” effect referred to as fundamental, intrinsic time (FIT).
Every elliptical shape (which is the fundamental construct of all of the phenomena that exists) is related by the Elliptical Constant (EC); if otherwise, how else could there be the resonance within a Pulsoid? This resonance results in the perfection of the Resoloid from which all observed phenomena is derived.

It is the geometry of the EC, which underlies the Conceptual Unit. It is the Conceptual Unit that sets the resonance of seminal motion (SM) that creates the "escapement effect" that creates the "clock" that measures fundamental, intrinsic time (FIT) that synchronizes the pulse of the Pulsoid.
The Elliptical Constant is the Rosetta Stone for all Knowledge and Wisdom; as, it is the EC that supports the logic of the universal Proof of One, which rationalizes the concepts of the Pulsoid Theory as a significant candidate for the theory of everything (TOE).

Some other corollaries of the Elliptical Constant (EC), in addition to the universal Proof of One, are: Conceptual Ellipses, the Brunardot Series, the revised Fibonacci sequence, the orthogonal dimensions, the Inverse Square Law, and the internal geometry of a light wave.

It is the Pulsoid Theory that: 1.) Redefines Pure Mathematics, which is a foundation for all physical theory; 2.) Explains the amazing mathematics of: the photon effect; subatomic and chemical bonds; “dark” energy; and “dark” matter; etc.; 3.) And, thus, ultimately unites Science, Theology, and Philosophy.

Despite the keen logic of Kurt Gödel, the Elliptical Constant demonstrates that it is possible to determine the value of any element of a system, including One, within the system itself, by establishing One as per the universal Proof of One. The significance of this observation concerning the Elliptical Constant and the universal Proof of One is that every physical manifestation evolves from the ellipse.

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The power of the Elliptical Constant is demonstrated by the vector radius, “oV,” of the above inscribed circle, CDH, which is an integer that equals one-half the sum of the amplitude (Line CF) minus the perigee (Line EB) for any Pulsoidal Ellipse (PE). And, of course, similarly, the hypotenuse radius, "Hr," is equal to the Key (Line oP), which is an integer multiple of the Elliptical Constant (h - w, 2p - r, etc.).

The Elliptical Constant (εpsilon = One)
can be expressed in many ways such as:
from the Brunardot Theorem, c² = 2v² – s²,
for any ellipse when v = εP²,
ε = v / P².
(ε = εpsilon; c = chord; s = soliton; v = vector; and P = Pulse)

Also, ε = P – K;
ε = h – w;
ε = 2P – r;
ε = v – r';
ε = h' – v
ε = w' – r; etc.
(K = Key; h = hypotenuse; h' = hypotenuse, acute; r = radius;
r' = radius, acute; w= wave; w' = wave, acute.)

Pulse Three Emergent Ellipse (Acute and Obtuse)

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Last edited by Epsilon=One : 08-13-2015 at 03:57 AM.
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Old 03-25-2008, 10:22 PM
Midgar21 Midgar21 is offline
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Default Re: Private Message on the Elliptical Constant, the Emergent Ellipsoid, and Infinity

The following is an excerpt of a correspondence posted for public view/interest.

Quote:
Originally Posted by Epsilon=One
How well do you understand, if at all from my sketchyness, the Emergent Ellipsoid?
When I say that I have studied the workings of the Elliptical Constant, I mean that I have studied the mathematics of it. I understand the proofs and derivations as to how it establishes a value of "1" as a constant within all ellipses

I have not, however, gone so far as to begin attempting to comprehend the existential notions of the Elliptical Constant--anything that implies that ellipses are the quintessential units of Reality is inherently suspect, mainly because at this point, I do not know enough about PT to infer that, in fact, they actually might be. Thus, I am not sure how certain aspects of ellipses could "quickly converge" under certain situations (an ellipse 'converging' implies elliptical movement as a physical, real phenomenon, involving actual quanta of matter).

My understanding (please advise if incorrect) of the "Emergent Ellipsoid" and 4xROI is as follows: Once the ROI is increased fourfold, the structural parts of the ellipse all become identifiable integers (because k=1 and e=1).

From this, I cautiously assume that, by your reasoning, the moment the salient structures of the ellipse are set as real/natural integers, an "Emergent Ellipsoid" is created--a quintessential building block of Reality. Again, this latter inference is, to me, not set in stone as of yet, as I have no further knowledge to support it aside from your word. Aside from that, however, the mathematics do support the notion that at 4xROI, an Emergent/Brunardot Ellipse is created. Now that I re-read this, I'm not I adequately explained much about Emergent Ellipses at all, but I leave that open to debate.

Quote:
Originally Posted by Epsilon=One
Are you thoroughly comfortable with my concept of Infinity? This is important; if their is uncertainty let me know. One of the biggest advances of PT is removing the "container" paradox from an understanding of the Universe. If I haven't been clear; or, if their is some disagreement, let me know.
I personally came to the conclusion that the Universe is commonly misperceived as a perpetual "container" in which cosmic "stuff" is put in. I believe this, and all other misconceptions of the Universe being a tangible, salient "object," as simply a result of the fallacy of human mental faculties, rather than human ignorance or pride. Your notion of Infinity, therefor, seems to be quite applicable. From what I understand, the Universe is simply all that is Reality--that which is not perpetual. That which is perpetual is Unreality, or rather, Infinity. Considering that the common element of everything in existence (Reality) is definable "motion," that which has no motion is thereby nonexistent and ergo, Infinite.

This is what I have taken from your notions of Infinity and the Emergent Ellipse. Clarification on your definition may be needed if I have misinterpreted it. As long as I know my interpretations are correct, I can progressively continue to analyze, scrutinize, understand, and organize Pulsoid Theory starting from strong foundational bases.
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Old 11-23-2008, 03:07 AM
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Epsilon=One Epsilon=One is offline
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Default I understand what you are saying; and, I can agree with your concerns.

Quote:
Originally Posted by Midgar21
[i][b]When I say that I have studied the workings of the Elliptical Constant, I mean that I have studied the mathematics of it. I understand the proofs and derivations as to how it establishes a value of "1" as a constant within all ellipses
Great !!!

Quote:
Originally Posted by Midgar21
I have not, however, gone so far as to begin attempting to comprehend the existential notions of the Elliptical Constant--anything that implies that ellipses are the quintessential units of Reality is inherently suspect, mainly because at this point, I do not know enough about PT to infer that, in fact, they actually might be. Thus, I am not sure how certain aspects of ellipses could "quickly converge" under certain situations (an ellipse 'converging' implies elliptical movement as a physical, real phenomenon, involving actual quanta of matter).
I understand what you are saying; and, I can agree with your concerns.

Quote:
Originally Posted by Midgar21
My understanding (please advise if incorrect) of the "Emergent Ellipsoid" and 4xROI is as follows: Once the ROI is increased fourfold, the structural parts of the ellipse all become identifiable integers (because k=1 and e=1).
Yes, exactly. The real significance, in the “real” world, beyond the heuristic model, is that at 4xROI there is a harmonic resonance. The motion (dimensions and forces have yet to fully evolve) of expansion is momentarily interrupted, as the motion is transferred to the resonance; thus momentarily stopping the expansion . . . which quickly continues; and the cycle continuously repeats from the point of interruption. This interruption of expansion is the “tick” of fundamental, intrinsic time (FIT).

Quote:
Originally Posted by Midgar
From this, I cautiously assume that, by your reasoning, the moment the salient structures of the ellipse are set as real/natural integers, an "Emergent Ellipsoid" is created
Not quite. The Emergent Ellipsoid begins as the first increment (from separation of a dimensionless point within a dimensionless sphere) evolves; at 4xROI (the Equilateral Emergent Ellipse) the phenomena of mass occurs which is an effect of the resonance.

Quote:
Originally Posted by Midgar21
--a quintessential building block of Reality.
In a sense. It is the first “building block” that exhibits the properties of mass. The first “building block”/seminal quantum exhibits the properties of “antimatter” and “space”

Quote:
Originally Posted by Midgar21
Again, this latter inference is, to me, not set in stone as of yet, as I have no further knowledge to support it aside from your word. Aside from that, however, the mathematics do support the notion that at 4xROI, an Emergent/Brunardot Ellipse is created. Now that I re-read this, I'm not I adequately explained much about Emergent Ellipses at all, but I leave that open to debate.
The salient concept of the Emergent Ellipse is that it is formed by two sets of foci each at the end of a pulse that emanates from the periphery and the center. Of course, the Pulse is also bi-directional from the foci . . . and along the 4 equal vectors. The geometry of an ellipse is such that all motion that emanates from a focus is redirected to its opposing focus. Thus the creative motion of an Emergent Ellipse is entirely self-contained.

Quote:
Originally Posted by Midgar21
I personally came to the conclusion that the Universe is commonly misperceived as a perpetual "container" in which cosmic "stuff" is put in. I believe this, and all other misconceptions of the Universe being a tangible, salient "object," as simply a result of the fallacy of human mental faculties, rather than human ignorance or pride. Your notion of Infinity, therefor, seems to be quite applicable. From what I understand, the Universe is simply all that is Reality--that which is not perpetual. That which is perpetual is Unreality, or rather, Infinity. Considering that the common element of everything in existence (Reality) is definable "motion," that which has no motion is thereby nonexistent and ergo, Infinite.
My belief is that the Universe is bounded, within and without, by Infinity. Thus, if you look inward or outward, you are looking into the same place. You will not “see” the back of your head if you look far enough. You will be looking back into the Universe at the perceived location of the “source” of gravitational phenomena.

Thus, as the Universe shares a locus with Infinity, it too is perpetual. That is, all the motion that enters the Universe dissipates to the same source from which it enters. How else can you explain where radiant energy “goes to”? Or, why the galactic clusters are receding at an . . . accelerating rate?

Quote:
Originally Posted by Midgar21
This is what I have taken from your notions of Infinity and the Emergent Ellipse. Clarification on your definition may be needed if I have misinterpreted it. As long as I know my interpretations are correct, I can progressively continue to analyze, scrutinize, understand, and organize Pulsoid Theory starting from strong foundational bases.
You are doing amazing well. Much better, and faster, than I when I first began such thoughts in the early ‘50s.

I have referenced/cited little in this reply, I anticipate much follow up.

Sorry, about my delay in replying. Of necessity, I’ve had to reduce my work load . . . and the mind seems to be a little slower and less sharp.
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