...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 = +2 

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

 =

 2

2

2

2

2

2

Alpha (Any Integer)

h

 =

4

4

4

4

4

4

Harmonic f(A)

i

 =

3

5

7

5

7

9

Brunardot Iteration
f(A)

inc.

=

2

2

2

2

2

2

Increment f(i)

T

 =

1

3

6

3

6

10

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

p

 =

5

13

25

13

25

41

 

s

 =

20

156

600

156

600

1640

Fibonacci

v

 =

25

169

625

169

625

1681

Sequence

a

 =

45

325

1225

325

1225

3321

 

r

 =

9

25

49

25

49

81

Generating

d

 =

41

313

1201

313

1201

3281

Right

l

 =

40

312

1200

312

1200

3280

Triangle

U

 =

1

1

1

1

1

1

Natural Unit

HR

=

10

78

300

78

300

820

Harmonic Ratio

e

=

225

4225

30625

4225

30625

136161

Internal Energy f(p)

F

=

15

65

175

65

175

369

Force


Minor Harmonics: None

 

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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