...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

 =

112

112

112

112

112

112

112

112

Harmonic f(A)

i

 =

15

97

111

113

**  127

209

223

225

Brunardot Iteration
 f(A)

inc.

=

14

82

14

2

14

82

14

2

Increment f(i)

T

 =

1

42

55

57

72

195

222

226

Tau: f(h,i); f(A)

p

 =

113

4705

6161

6385

8065

21841

24865

25313

 

s

 =

12656

22132320

37951760

40761840

65036160

477007440

618243360

640722656

Fibonacci

v

 =

12769

22137025

37957921

40768225

65044225

477029281

618268225

640747969

Sequence

a

 =

25425

44269345

75909681

81530065

130080385

954036721

1236511585

1281470625

 

r

 =

225

9409

12321

12769

16129

43681

49729

50625

Generating

d

 =

25313

44264641

75903521

81523681

130072321

954014881

1236486721

1281445313

Right

L

 =

25312

44264640

75903520

81523680

130072320

954014880

1236486720

1281445312

Triangle

U

 =

1

1

1

1

1

1

1

1

Natural Unit

HR

=

226

395220

677710

727890

1161360

8517990

11040060

11441476

Harmonic Ratio

v2

=

163047361

490047875850625

1440803766642241

1662048169650625

4230751205850625

227556934931376961

382255598044650625

410557959777624961

Vector Energy

s2

=

160174336

489839588582400

1440336087097600

1661527600185600

4229702107545600

227536097815353600

382224852184089600

410525521911694336

Soliton Energy

E

=

2873025

208287268225

467679544641

520569465025

1049098305025

20837116023361

30745860561025

32437865930625

Internal Energy

F

=

1695

456385

683871

721505

1024255

4564769

5544895

5695425

Force

c2

=

165920386

490256163118850

1441271446186882

1662568739115650

4231800304155650

227577772047400322

382286343905211650

410590397643555586

Chord Energy


Minor Harmonics for +8: None

 

**Note: Fifth Increment
   Red Numerals are
   the same for BHE -8

 

 

 

 

A

=

Alpha (motion = y-axis)

l

=

Light

a = apogee M = Mean (s2 / v)
c = chord, major o = opposing wave crest
d = diagonal p = perigee
E = Energy, Internal r = radius
f = Force s = soliton
H = Harmonic T = Tau (time, etc. = x-axis)

HR

 = Harmonic Ratio

CU

 = Conceptual Unit
i = Brunardot Iteration v = vector
I = Infinity line (x-axis) w = wave crest
inc. = increment between "i"s x = foci
K = 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 . . .

in   = in-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









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and, a manifestation of the
 Unified Concept; thus;

. . . the Fundamental Postulate.


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