The Pulsoidal Ellipse

[Epsilon=One]

The Pulsoidal Ellipse (PE)

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http://b.g2d.us/peo-600.gif
http://b.g2d.us/pea-600.gif
Legend for a Pulsoidal Ellipse (PE)

Line AD = BJ = radius = r
Line BA = hypotenuse = h
Line BC = CD = soliton = s
Line BD = wave = w
Line BF = DH = vector = v
Line CA = JC = diagonal radial = d
Line CF = CH = amplitude = a = Natural integer (www.101123.com/NI) if PE
Line DI = epsilon = e
Line EB = DG = perigee = p
Line EC = CG = major radial = m
Line ED = BG = apogee = o
Line EF = EH = diameter chord = C only a Natural Integer (www.101123.com/NI) if UE
Line EG = major diameter = M
Line GI = key = k
Line FH = minor diameter = L
Line JA = diagonal = D
Line oK = Hypotenuse radius = Hr = Natural integer (www.101123.com/NI) if BE
Line oL = Vector radius = Vr = Natural integer (www.101123.com/NI) if PE
Line oN = Chord radius = 2Cr = Cd Natural integer (www.101123.com/NI) if PE
Triangle ABD = Brunardot triangle (www.101123.com/BTr) (One of a pair)
Triangle CDH = Pythagorean triangle (www.CQthus.com/PTr)
Triangle CEH = only is a Pythagorean triangle (www.CQthus.com/PTr) if it is an Ultron Ellipse (www.101123.com/UE) (UE)
Inscribed circle ABD = Hypotenuse circle
Inscribed circle CDH = Vector circle
Inscribed circle CEH = Chord circle
p, s, v, o = 1st terms of a Brunardot Series (www.101123.com/BS)
The Pulsoidal Ellipse (PE) is a Brunardot Ellipse (www.101123.com/BE) that has a Natural integer (www.101123.com/NI) value for the amplitude, "a" (Line CF).

Pulsoidal Ellipses (PE) comprises an unending sequence; and, each PE can be mapped to a unique, sequential Brunardot Ellipse (www.101123.com/BE) (BE), which can be generated by any Natural integer (www.101123.com/NI).

The Vector radius (Line oV) is, also, a Natural integers (www.101123.com/NI).

The Vector diameter (2 times Line oV) equals the amplitude, "a," minus the perigee, "p."

The Chord diameter (2 times Line oT) quickly converges to a Natural integer as the perigee (Line EB) increases.

The Chord diameter quickly converges to the amplitude, "a," minus the perigee, "p." plus One, "1."

Vd = a - p........
Td = a – p + 1........

From the Brunardot Ellipse (www.101123.com/BE):
The Hypotenuse radius equals the perigee minus one; or,
the radius minus the perigee; or,
one-half the sum of the radius minus one . . . or,
the apogee minus the hypotenuse.
Pr = p – 1; or,
(r – 1) / 2; or,
r – p; or,
o – h

Ultimate simplicity has been found;
at the crux of . . . complexity!!!
........................
The three inscribed circle diameters are all Natural integers (www.101123.com/NI) found with simple addition and subtraction that involves only one, "1," the amplitude, "a," and the perigee. "p," of a Pulsoidal Ellipse (PE).

One must ask:........................................
Why ?
And, again,
Why ?
And, again,
Why ?
Over and over,
until . . . Infinity.

The Pulsoidal Ellipse (PE) is, heuristically, associated with the Congeneric Realm of Propagation (www.101123.com/CRR).

See: Conceptual Ellipses (www.101123.com/CE) (CE), Brunardot Ellipses (www.101123.com/BE) (BE),
.......Ultron Ellipses (www.101123.com/UE), and Mystique of the Ellipses (www.101123.com/Em);
.......the Brunardot and Ultron Ellipses, heuristically,
.......represent natural ellipsoidal quantum that manifests as forms of matter/mass.

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Terms: PhysicsMathForums.com, Brunardot, and Pulsoid Theory must be cited.
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[ste]

1) Point "I" does not exist.
2) Line segment "BF" does not exist
3) Line segment "DI" does not exist (see 1)
4) Line segment "GI" does not exist (see 1)

[Epsilon=One]

1) Point "I" does not exist.
2) Line segment "BF" does not exist
3) Line segment "DI" does not exist (see 1)
4) Line segment "GI" does not exist (see 1)You are correct. I switched images as this post was originally prior to the post that introduced the concept of acute and obtuse Emergent Ellipses.

I will corrrect the entire post in a day or two. Until then, Line BF should be Line BH = DH = Vector, "v," on the top obtuse ellipse. The lower acute ellipse is not entirely labelled.

Thank you for proofreading. All posts are rapidly created with little rereading.

Line DI was originally Line AB = hypotenuse, "h," minus Line BD = wave, "w," = ε = One, "1."

In the current image, ε = Line DG minus Line oK.

I will clarify with revision of post.
prior to

[ste]

How are Pulsoidal Ellipses associated with the Con ge neric Realm of Propagation? What natural phenomenon can they be used to heuristically explain? Why does it matter which quadrant the inscribed circles are in? Are the inscribed circles analogous to quarks or leptons?

[Epsilon=One]

How are Pulsoidal Ellipses associated with the Con ge neric Realm of Propagation? What natural phenomenon can they be used to heuristically explain?Pulsoidal Ellipses (PE) are formed when the amplitude, "a," is an integer; thus, creating a reinforcing resonance to the vector resonance. These two resonances quickly merge as the pulses increase.

Quite interestingly, the amplitude, "a," is an integer when the Pulse, "P," is equal to the hypotenuse, "h," of any obtuse/inertial Brunardot Ellipse (www.CQthus.com/PT/BE) (BE).

Why does it matter which quadrant the inscribed circles are in? Are the inscribed circles analogous to quarks or leptons?The quadrant doesn't matter. The characteristic of the resonance is determined by which motion is involved as the hypotenuse of the involved right triangle.

The resonances are analogous to fermions. When ejected, they are analogous to bosons.