...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

 

 

 

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









E-mail :  Brunardot@Brunardot.com







There is one Universe.

It is perpetual, in equilibrium; and,

a manifestation of the . . . Unified Concept;


also,

are a single discipline, which proclaims the

perpetuity and nexus of Life; such is


. . . Conceptualism.





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