A

 =

-4

-3

-2

-1

0/1

2

3

4

5

10

79

136

23133

Alpha (Any lnteger)

p

 =

41

25

13

5

1  

5

13

25

41

181

12325

36721

1070225113

Conceptual

s

 =

1640

600

156

20

0  

20

156

600

1640

32580

151893300

1348395120

1145381791425637656

Fibonacci

v

 =

1681

625

169

25

1  

25

169

625

1681

32761

151905625

1348431841

1145381792495862769

Sequence

a

 =

3321

1225

325

45

1  

45

325

1225

3321

65341

303798925

2696826961

2290763583921500425

Ellipse

r

 =

81

49

25

9

1  

9

25

49

81

361

24649

73441

2140450225

Generating

d

 =

3281

1201

313

41

1  

41

313

1201

3281

65161

303786601

2696790241

2290763582851275311

Right

L

 =

3280

1200

312

40

0  

40

312

1200

3280

65160

303786600

2696790240

2290763582851275312

Triangle

U

 =

1

1

1

1

1  

1

1

1

1

1

1

1

1

Natural Unit

v2

=

2825761

390625

28561

625

1  

625

28561

390625

2825761

1073283121

23075318906640625

1818268429822649281

1311899450581035638132483981680347361

Vector Energy

s2

=

2689600

360000

24336

400

0  

400

24336

360000

2689600

1061456400

23071574584890000

1818169399639814400

1311899448129402922673811206205174336

Soliton Energy

E

=

136161

30625

4225

225

1  

225

4225

30625

136161

11826721

3744321750625

99030182834881

2451632715458672775475173025

Internal Energy

F

=

369

175

65

15

1  

15

65

175

369

3439

1935025

9951391

49513964852945

Force

c2

=

2961922

421250

32786

850

2  

850

32786

421250

2961922

1085109842

23079063228391250

1818367460005484162

1311899453032668353591156757155520386

Chord Energy

UF

=

 40

 24

12

4

1  

4

12

24

40

180

12324

36720

1070225

Unimetric Factor

M

=

 1600

 576

144

16

1  

16

144

576

1600

32400

151880976

1348358400

1145381550625

Mean

H

=

 20

 12

6

2

1  

2

6

12

20

90

6162

18360

535112556

Harmonic

HR

=

 9

 7

5

3

1  

3

5

7

9

19

157

271

46265

Harmonic Ratio

IF

=

 41

 25

13

5

1  

5

13

25

41

181

12325

36721

1070225113

Iteration Factor

IR

=

 1

 1

1

1

1  

1

1

1

1

1

1

1

1

Iteration Ratio

T

=

 2

 2

2

2

--  

2

2

2

2

2

2

2

2

Tau

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

000101 0:02 am