...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 = 112 112 112 112 112 112 112 112 Harmonic f(A) i = 15 97 111 113 **  127 209 223 225 Brunardot Iteration  f(A) inc. = 14 82 14 2 14 82 14 2 Increment f(i) T = 1 42 55 57 72 195 222 226 Tau: f(h,i); f(A) p = 113 4705 6161 6385 8065 21841 24865 25313 s = 12656 22132320 37951760 40761840 65036160 477007440 618243360 640722656 Fibonacci v = 12769 22137025 37957921 40768225 65044225 477029281 618268225 640747969 Sequence a = 25425 44269345 75909681 81530065 130080385 954036721 1236511585 1281470625 r = 225 9409 12321 12769 16129 43681 49729 50625 Generating d = 25313 44264641 75903521 81523681 130072321 954014881 1236486721 1281445313 Right L = 25312 44264640 75903520 81523680 130072320 954014880 1236486720 1281445312 Triangle U = 1 1 1 1 1 1 1 1 Natural Unit HR = 226 395220 677710 727890 1161360 8517990 11040060 11441476 Harmonic Ratio v2 = 163047361 490047875850625 1440803766642241 1662048169650625 4230751205850625 227556934931376961 382255598044650625 410557959777624961 Vector Energy s2 = 160174336 489839588582400 1440336087097600 1661527600185600 4229702107545600 227536097815353600 382224852184089600 410525521911694336 Soliton Energy E = 2873025 208287268225 467679544641 520569465025 1049098305025 20837116023361 30745860561025 32437865930625 Internal Energy F = 1695 456385 683871 721505 1024255 4564769 5544895 5695425 Force c2 = 165920386 490256163118850 1441271446186882 1662568739115650 4231800304155650 227577772047400322 382286343905211650 410590397643555586 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
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