Brunardot Harmonic Ellipses: Integer -8

...nature's thing for geometry has gotten so out of hand, some scientists would say, that she
has kissed fields such as physics goodbye for good.

Forget forces, particles, fields, gravity, matter, motion -- even space and time.

Physics has become a chapter in a geometry book.

"It almost appears that the physics has been absorbed into the geometry,"
wrote: Sir Arthur Eddington.

Los Angeles Times
November 4, 1999

Eddington: An English scientist involved in the fields of mathematics, relativity, cosmology, and astronomy. While professor of astronomy at Cambridge, he worked on the structure of stars. He also made significant and pioneering contributions to the general theory of relativity,

Limitless Series,
TABLE BHE: Integer = -8

BRUNARDOT HARMONIC ELLIPSES

with radius "r" and vector "v" as squares of integers; and, diagonal "d," perigee "p," and Brunardot Iteration "i," above the first iteration, as Natural Prime numbers; also, force "F," energy "E," and the Harmonic Ratio "HR" are integers; soliton "s" is an even integer and Light "L" is an integer divisible by 4; and also, included is a simple series and a right triangle; all components, so described, are generated by . . . any, single integer . . . with limitless iterations.
(Except for "0" and +1, which generate the quaquaversal axes of Reality.)

h=f(A), i=f(A), T=f(h,i); therefore, T = f(A)

A	=	1st Iteration 1st Cycle -8	2nd Iteration 1st Cycle -8	3rd Iteration 1st Cycle -8	4th Iteration 1st Cycle -8	1st Iteration 2nd Cycle -8	2nd Iteration 2nd Cycle -8	3rd Iteration 2nd Cycle -8	4th Iteration 2nd Cycle -8	Alpha (Any lnteger)
h	=	144	144	144	144	144	144	144	144	Harmonic f(A)
i	=	-17	161	143	145	** 127	305	287	289	Brunardot Iteration f(A)
inc.	=	-18	178	-18	2	-18	178	-18	2	Increment f(i)
T	=	1	90	71	73	56	323	286	290	Tau: f(h,i); f(A)
p	=	145	12961	10225	10513	8065	46513	41185	41761
s	=	20880	167974560	104540400	110512656	65036160	2163412656	1696163040	1743939360	Fibonacci
v	=	21025	167987521	104550625	110523169	65044225	2163459169	1696204225	1743981121	Sequence
a	=	41905	335962081	209091025	221035825	130080385	4326871825	3392367265	3487920481
r	=	289	25921	20449	21025	16129	93025	82369	83521	Generating
d	=	41761	335949121	209080801	221025313	130072321	4326825313	3392326081	3487878721	Right
L	=	41760	335949120	209080800	221025312	130072320	4326825312	3392326080	3487878720	Triangle
U	=	1	1	1	1	1	1	1	1	Natural Unit
HR	=	290	2332980	1451950	1534898	903280	30047398	23557820	24221380	Harmonic Ratio
v²	=	442050625	28219807211725441	10930833187890625	12215370885802561	4230751205850625	4680555575930170561	2877108772907850625	3041470150404416641	Vector Energy
s²	=	435974400	8215452807193600	10928695232160000	12213047136174336	4229702107545600	4680354320140974336	2876969058262041600	3041324491357209600	Soliton Energy
E	=	6076225	4354404531841	2137955730625	2323749628225	1049098305025	201255789196225	139714645809025	145659047207041	Internal Energy
F	=	2465	2086721	1462175	1524385	1024255	14186465	11820095	12068929	Force
c²	=	448126850	28224161616257282	10932971143621250	12217694635430786	4231800304155650	4680756831719366786	2877248487553659650	3041615809451623682	Chord Energy
		Minor Harmonics for -8: None				**Note: Fifth Increment Red Numerals are the same for BHE +8

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Alpha (motion = y-axis)

Light

apogee

Mean (s² / v)

chord, major

opposing wave crest

diagonal

perigee

Energy, Internal

radius

Force

soliton

Harmonic

Tau (time, etc. = x-axis)

Harmonic Ratio

Conceptual Unit

Brunardot Iteration

vector

Infinity line (x-axis)

wave crest

inc.

increment between "i"s

foci

Unimetric Factor

The following is true for:

Every integer value of
Alpha (A) except zero and +1

d	=	A Natural Prime number (Nature's Scale)
r	=	A Perfect square
L	=	An Integer divisible by four
d,r,L	=	A Right Triangle that Generates BHE's

a, c², d, f, i, L, p, and s and are integers.

	E, r, v, and U are perfect squares.
	d, i, and p are Natural Prime numbers.
	p, s, v and a are consecutive terms of a series.

p, s, and Tau are functions of Alpha.

An Infinity line "I" and a motion line "m" are at

right angles to one another and are both infinite in length and infinitesimal in width.

Corollary formulas derived from
the Brunardot Theorem: c² = 2v² - s²

Primary Corollaries:
	U = d - L = 1	The Natural Unit, U, establishes the relative unit value for all other integers.

U = A Proof of One.

The Integer One is a Relativistic Function of Alpha (Motion) and Tau. (Speed, Spin, Space, and Time)

h = 2(A² - A); or, A² - A

i₁= 2A - 1	i₁= square root of (2h + 1)
i₂ = 2A² - 4A + 1;	i₂= h - (2A - 1) = h - i₁
i₃ = 2(A²-A) - 1;	i₃= h - 1
i₄ = 2(A²-A) + 1;	i₄= h + 1
i₅ = 2A² - 1;	i₅= h + i₁;	i₅ =i₁ + h . . .
i₆ = 4A² - 6A + 1;	i₆= 2h - i₁;	i₆=i₂ + h . . .
i₇ = 4A² - 4A - 1;	i₇= 2h - 1;	i₇=i₃ + h . . .
i₈ = 4A² - 4A + 1;	i₈= 2h + 1;	i₈=i₄ + h . . .
i₈ = (2A - 1)²= i²		i₁₂=i₈ + h . . .
		i_n=i_n-4 + h . . .

Tau (T) = ((i² - 1) / 2) / 2A(A - 1)

Tau (T) = (((i² + 1) / 2) - 1) / h

Tau (T) = L / 2hp

Tau (T) = (p - 1) / h

p = (i² + 1) / 2

s = p² - p

v = p+ s

a = s+ v

M = s² / v

r = i²; or, v - M

d = (i⁴ + 1) / 2; or 2M + r

L = d - 1

HR= L / h

E = v² - s²

F = square root of E

c² = E + v²

And, thus, some Secondary Corollaries:

a = 2p² - p

a = 2s + p

c² = 2E + s²

c² = F² + v²

d = L + 1

d = L + 2p - r

d = r² - L

d = 2v - r

d = i⁴ - L

E = rv

E = c² - v²

E = ( c² - s²) / 2

E = F²

F = square root of c² - v²

F = square root of v² - s²

F = square root of rv

F = ip

HR = T(r + 1)

HR = 2pT

L = i⁴ - d

L = (i⁴ - 1) / 2

L = 2hpT

p = 2AT (A - 1) + 1 = hT + 1

p = (i² + 1) / 2

p = L / 2hT

r = 2v - d

r = 2p - 1

r² = d + L

s = (i⁴ - 1) / 4

s = p(p - 1)

s² = v²- E

U = 2p - r

U = i⁴ - 2L

U = i⁴ - 4hpT

U = p - 2AT (A - 1)

U = HR /T - r

U = p - hT

v = p²

v = E / r

v² = E + s²

v² = (c²+ s²) / 2

There is one Universe.

It is perpetual, in equilibrium;

and, a manifestation of the
Unified Concept; thus;

. . . the Fundamental Postulate.

also,

Science, Theology, and Philosophy

are a single discipline, Philogic,
which proclaims perpetuity

and the nexus of Life; such is

. . . Conceptualism.

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