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#1
08-06-2005, 03:27 AM
 Epsilon=One Senior Member Join Date: Jul 2005 Location: Orange County, California Posts: 2,117
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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Terms: PhysicsMathForums.com, Brunardot, and Pulsoid Theory must be cited.
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"Seek simplicity; and
. . . Natural integers."

...c² = 2v² – s²........v = εP²

Last edited by Epsilon=One : 02-10-2008 at 10:58 PM. Reason: format
#2
07-07-2006, 08:28 PM
 Albers Senior Member Join Date: Feb 2006 Location: southern Oregon Posts: 208

This is geometric rock and roll. I'm with you up 'til the generalization to different ellipses. I look forward to spending more time, as your presentations are more and more developed. Just in fun I told you 'one' sucked, and you had to double it! Ha, ha.
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Last edited by Albers : 07-07-2006 at 08:32 PM.
#3
07-07-2006, 08:39 PM
 Epsilon=One Senior Member Join Date: Jul 2005 Location: Orange County, California Posts: 2,117
Elaborate a bit.

Quote:
 Originally Posted by Albers This is geometric rock and roll. I'm with you up 'til the generalization to different ellipses.
Not sure what you mean.

I'd love to discuss the situation if you'll elaborate a bit.
__________________
..."Click" to E-mail Me Directly
.....Also, my forum Private Msg box,
..........finally, is now working.
"Seek simplicity; and
. . . Natural integers."

...c² = 2v² – s²........v = εP²
#4
10-29-2006, 12:24 PM
 Albers Senior Member Join Date: Feb 2006 Location: southern Oregon Posts: 208

Can you relate to these recent thoughts on radiating atoms? Consider a barber pole where blue and red are 180 degrees opposite, and are electrically oppositely charged. This may be pictured as a helix of adjacent dipoles. If such a structure is rotated at "coincident" speed (given light propagation), then radiation will be projected in one direction, predominately, namely the one in which the "screw thread" appears to move (it's phase motion). You can see this by considering the image of one dipole projected both ways. Going backwards there is cancellation with the subsequent position; this is a "retarded time" problem. What is germain for us is that the simplest unit of construction with which we can see this consists of two dipoles 90 degrees out of phase, rotating as a rigid tetrahedron about a symmetry axis. Visualize a plane cutting the midpoints of four edges. This is the minimum directional radiator.
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#5
10-29-2006, 06:21 PM
 Epsilon=One Senior Member Join Date: Jul 2005 Location: Orange County, California Posts: 2,117
Your visualization is analogous to how I visualize the resonance groups.

Quote:
 Originally Posted by Albers Can you relate to these recent thoughts on radiating atoms?
Yes, referring to what you state below. Can you refer to a source for the "barber pole" analogy?

Quote:
 Originally Posted by Albers What is germain for us is that the simplest unit of construction with which we can see this consists of two dipoles 90 degrees out of phase, rotating as a rigid tetrahedron about a symmetry axis. Visualize a plane cutting the midpoints of four edges. This is the minimum directional radiator.
Your visualization is analogous to how I visualize the resonance groups (Resoloids) within a Pulsoid; except that, your "rotating" I visualize as pulsating (there is difficulty in synchronizing four resonances as a "rigid tetrahedron about a symmetry axis".

I visualize three major tetrahedron groups for a total of twelve major resonance/particles. The groups are designated as the hypotenuse and vector groups for the obtuse "envelope" of the Emergent Ellipsoid and the hypotenuse group for the acute "envelope" of the Emergent Ellipsoid.

I don't understand how you are relating this post to the Elliptical Constant? Though, I relate ALL fundamental phenomena to the Elliptical Constant; which includes . . . the singularity!
__________________
..."Click" to E-mail Me Directly
.....Also, my forum Private Msg box,
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"Seek simplicity; and
. . . Natural integers."

...c² = 2v² – s²........v = εP²
#6
10-29-2006, 06:38 PM
 Albers Senior Member Join Date: Feb 2006 Location: southern Oregon Posts: 208

The barber pole is my own visualization of helical charge envelopes. Feynman in Vol. I, 29-4, talks of interfering dipole radiation to set the stage here. No I don't yet deal in your system and am just hoping to enjoy some resonance of ideas! I shall investigate this in terms of spherical geometry and harmonics. The point is, it is the time-dependent radiating state and so not to be constructed as a time-independent pattern. In QM we construct the interference state integral of psi*(b)OPpsi(a) and I see this as literally the expression of how an atom is an antenna. In the present instance there is not a simple dipole moment, but one that is rotated in the z-direction. I'll let you know.
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Last edited by Albers : 10-29-2006 at 06:45 PM.
#7
10-29-2006, 06:52 PM
 Epsilon=One Senior Member Join Date: Jul 2005 Location: Orange County, California Posts: 2,117
Elliptical motion in real time is helical motion.

Quote:
 Originally Posted by Albers The barber pole is my own visualization of helical charge envelopes. Feynman in Vol. I, 29-4, talks of interfering dipole radiation to set the stage here.
Vol I, Feynman Lectures??? Elliptical motion in real time is helical motion because a moving ellipse does not "close."

Quote:
 Originally Posted by Albers I shall investigate this in terms of spherical geometry and harmonics.
Great!!! See if you can come up with the slide, swing, and vibration of Triquametric motion that creates the Emergent Ellipsoidal quantum.

Quote:
 Originally Posted by Albers The point is, it is the time-dependent radiating state and so not to be constructed as a time-independent pattern.
Is there anything that exists that is "time-independent"?
__________________
..."Click" to E-mail Me Directly
.....Also, my forum Private Msg box,
..........finally, is now working.
"Seek simplicity; and
. . . Natural integers."

...c² = 2v² – s²........v = εP²
#8
10-29-2006, 08:45 PM
 Albers Senior Member Join Date: Feb 2006 Location: southern Oregon Posts: 208

Quote:
 Originally Posted by Epsilon=One Vol I, Feynman Lectures??? Elliptical motion in real time is helical motion because a moving ellipse does not "close." Great!!! See if you can come up with the slide, swing, and vibration of Triquametric motion that creates the Emergent Ellipsoidal quantum. Is there anything that exists that is "time-independent"?
Is there any definable form?
__________________
The string uncut and unstrung has no note.
#9
10-29-2006, 10:40 PM
 Epsilon=One Senior Member Join Date: Jul 2005 Location: Orange County, California Posts: 2,117
There must be a defineable form; and, it is the ellipsoid.

Quote:
 Originally Posted by Albers Is there any definable form?
Fundamentally, Yes.

There must be a defineable form; and, it is the ellipsoid.

If not, there would be no quantum; nor, a definition of One.
__________________
..."Click" to E-mail Me Directly
.....Also, my forum Private Msg box,
..........finally, is now working.
"Seek simplicity; and
. . . Natural integers."

...c² = 2v² – s²........v = εP²

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