...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 = +15 

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
 15

* 2nd Iteration
1st Cycle
15

3rd Iteration
1st Cycle
15

4th Iteration
1st Cycle
15

1st Iteration
2nd Cycle
15

2nd Iteration
2nd Cycle
15

3rd Iteration
2nd Cycle
15

4th Iteration
2nd Cycle
15



Alpha (Any lnteger)

h

 =

420

420

420

420

420

420

420

420

Harmonic f(A)

i

 =

29

391

419

421

**  449

811

839

841

Brunardot Iteration
 f(A)

inc.

=

28

362

28

2

28

362

28

2

Increment f(i)

T

 =

1

182

209

211

240

783

838

842

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

p

 =

421

76441

87781

88621

100801

328861

351961

353641

 

s

 =

176820

5843150040

7705416180

7853593020

10160740800

108149228460

123876193560

125061603240

Fibonacci

v

 =

177241

5843226481

7705503961

7853504400

10160841601

108149557321

123876545521

125061956881

Sequence

r

 =

841

152881

175561

177241

201601

657721

703921

707281

Generating

d

 =

353641

11686300081

15410832361

15707186041

20321481601

216298456921

247752387121

250123206481

Right

L

 =

353640

11686300080

15410832360

15707186040

20321481600

216298456920

247752387120

250123206480

Triangle

U

 =

1

1

1

1

1

1

1

1

Natural Unit

HR

=

842

27824524

36692458

37398062

48384480

514996326

589886636

595531444

Harmonic Ratio

E

=

149059681

893318307641761

1352785980897121

1391994387732481

2048435827603201

71132234990725441

87199301799687941

88453945924750561

Internal Energy

F

=

12209

29888431

36780239

37309441

45259649

266706271

295295279

297412081

Force

2

2

* Minor Harmonics for +15, 1/2 h = 210: 2nd Iteration = 12-30-68-30-12 = 152 (Double Values for h = 420)

**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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