Table BE2:
                            BRUNARDOT's ELLIPSES
                                   Generated by Any Two Integers
     F = integer, p = f(A,T ), s = f(A,T )


...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, 

A

 =

 1

 2

 3

3

9

12

13

7

Any lnteger

T

 =

1

1

2

6

5

5

6

14

Any Integer

p

 =

5

20

117

765

4941

8784

14365

20629

 

s

 =

20

80

1404

64260

296460

527040

1206660

8664180

Fibonacci

v

 =

25

100

1521

65025

301401

535824

1221025

8684809

Sequence

a

 =

45

180

2925

129285

597861

1062864

2427685

17348989

 

r

 =

9

36

225

1521

9801

17424

28561

41209

Generating

l

 =

40

160

2808

128520

592920

1054080

2413320

17328360

Right

d

 =

41

164

2817

128529

593001

1054224

2413489

17328409

Triangle

U

 =

1

4

9

9

81

144

169

49

Natural Unit

A

=

1

2

3

3

9

12

13

7

Sq Root U

i

=

3

6

15

39

99

132

169

203

Sq Root  r

F

=

15

60

585

9945

54351

96624

186745

598241

Force

c2

 =

850

13600

2655666

4327153650

93796594002

296443556352

1525775745650

75783799660562

Brunardot's

s2

 =

400

6400

1971216

4129347600

87888531600

277771161600

1456028355600

75072139278724

Theorem

2v2

 =

1250

20000

4626882

8456501250

181685125602

574214717952

2981804101250

150855938939286

 

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


d = Natural Prime number (Nature's Scale)
r = Square)
L = Integer divisible by four


a, d, f, i, L, p, s, v and c2 are integers.
r and U are squares.
p, s, v and a are consecutive terms of a series.
p and s are functions of Alpha and Tau.


An Infinity line, I, is infinite in length
and infinitesimal in width.

Corollary formulas to Brunardot's Theorem:

Primary Corollary: U = A2

r = 2p - 1

L = 2s

d = L + 1

v = p2

a = 2p2 - p

c2  = 2v2 - s2

e = v2 - s2

x = p/s

F = square root of e

And, thus:

U = d - Lv = s + p

U = 2p - r

v = s + p

r = 2v - d

c2  = f2 + v2

d + r = L + 2p

a = 2s + p

e = ( c2 - s2)/2









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It is perpetual, in equilibrium;

and, a manifestation of the
 Unified Concept; thus;

. . . the Fundamental Postulate.


also,

are a single discipline, Philogic,
which proclaims perpetuity

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