More Notes on Proportion

SOLITU PX: more detailed evidence of Evolutionary Proprotion:

Here are more notes on the "proportion is everything" experience:

WILL YOU SEE WHAT I SEE? THIS IS THE MEANING OF PROPORTION. WE SEE IT WHEN WE SEE THE VINES TWINING, THE PATTERNS OF LEAF NODES ON A STEM AND THE SUNFLOWER SEEDS IN THE POD. THE SPIRAL CURVES INSIDE THE NAUTILUS, THE GOLDEN SECTION IN ALL LIVING THINGS, AND WHEN WE LOOK AT THE DIGITAL OUTPUT OF THE MANDELBROT SET AND WE SEE THE FAMILIAR ORGANIC SHAPES OF FROST AND NEEDLES AND PAISLEY PATTERNS AND THE BRANCHES OF TREES AND RIVERS -- ALL THIS WE SEE IN THE GEOMETRIC SHAPES, BUT HERE I ENDEAVOR TO SHOW THAT WE CAN SEE THIS SAME PATTERN OF PROPORTION IN NUMBERS. THE REALITY OF PHYSICS AND THE NATURAL WORLD, THE REAL, PHYSICAL UNIVERSE IS THAT OUR EYES DETECT A NARROW SLICE OF THE ELECTROMAGNETIC SPECTRUM AND WE NAME THAT PERCEPTION "GREEN." OUR EARS DETECT A NARROW SLICE OF THE VIBRATIONAL SPECTRUM AND WE NAME THAT PERCEPTION "HIGH C" OR "MEADOWLARK." SO WHAT I AM TRYING TO TEACH THE WORLD IS THAT WHEN WE DETECT A PARTICULAR PROPORTION WE NAME THAT PERCEPTION "FIVE." MATHEMATICS IS A LANGUAGE, A VOCABULARY TO DESCRIBE PROPORTIONS, AND COUNTING AND MEASURING PROPORTIONS. I AM SAYING THAT THIS IS WHAT MATHEMATICS IS. AND THAT MEANS MATHEMATICS IS A CULTURAL INVENTION, A PRODUCT OF THE HUMAN INTELLECT, NOT A PRODUCT OF THE COSMOS. PROPORTION IS NOT A PRODUCT OF THE COSMOS. PROPORTION IS THE ORIGIN OF THE COSMOS, AND OUR MATHEMATICS IS OUR LANGUAGE FOR TALKING ABOUT PROPORTION. ANOTHER DIFFERENT LANGUAGE FOR TALKING ABOUT PROPORTION IS POSSIBLE, BUT PROPORTION IS THE TRULY UNIVERSAL LANGUAGE BECAUSE ALL PROPORTIONS ARE THE SAME FOR ALL PERCEIVING INTELLECTS. ANOTHER SPECIES CAN HAVE ANOTHER WORD FOR "FIVE" BUT CANNOT HAVE ANY OTHER PERCEPTION FOR FIVE EXCEPT THE FIVE THAT IS FIVE EVERYWHERE WITHIN THE ONE BIG SETTING THAT WE CALL THE UNIVERSE.

While studying the relationship of 3.84 to other pi values: 3.84 = pi*MQ*S4,

where S4 = (sec 18)^4, noted that 0.96 = (24/25) and (24/25) * 4 = 3.84

and therefore: (24/25) * 4 = pi*MQ*S4, then (96/25) = pi*MQ*S4

and then pi = . 96 . and this is correct because:

25*S4*MQ

(pi*MQ) = (pi*D) = (9/5) + sqrt(9/5) = 3.1416407864998738178455042012388

= pi * 1.0000153211811294438540391539833 same as pi * MQ

and . 96 . = . 3.84 .

25*S4*MQ 1.2223099629457561787050273027009

= 3.1415926535897932384626433832796 = pi exactly

First short pi-line list, and new pi-lines as sqrt [ (pi*A) * (pi*B) ]

A-LT 1) 3.1406228624894574694952341031297 [ 2 + sqrt(5) ] – sqrt(6/5)

B-LT 2) 3.141320000468716979810539729062 [ sqrt(37) – 1] * (1/phi)

C-LT 3) 3.1414803893897418379555528189649 [ sqrt(LT 2 * GT 1) ]

D-GT 1) 3.1416407864998738178455042012388 [ (9/5) + sqrt(9/5)] (pi*MQ)

E-GT 2) 3.14181818181818181818181818181821[(1/0.55*1.728] Pi*MQ*TN

F-GT 3) 3.1446055110296931442782343433718 [ sqrt(1/phi) * 4 ] (pi*Ho)

A/pi= 0.99969130590523006826067955285487, R= 1.000308789416239252250953621567

B/pi= 0.99991321181606256081092289835142, R= 1.0000867957167800720798498745267

C/pi= 0.99996426519525912439773056310645, R= 1.0000357360817627795991640069671

D/pi= 1.0000153211811294438540391539833, R= 0.99998467905360555092981479443066

E/pi= 1.0000717878647096007586587022098, R= 0.99992821728841798677919783611326

F/pi= 1.0009590223087825259636982582862, R= 0.99904189653381566667643734461942

Square root summary (six starting values, as above):

Sqrt(A*B)/pi = 0.99980225270414974513874977313682

Sqrt(A*C)/pi = 0.99982777623529363214445554687244

Sqrt(A*D)/pi = 0.99985330041801700928533696136481

Sqrt(A*E)/pi = 0.99988152878701072493631342496175

Sqrt(A*F)/pi = 1.00032496328417652881857146469

Sqrt(B*C)/pi = 0.99993873817983494104610765842083

Sqrt(B*D)/pi = 0.99996426519525912439773056310646

Sqrt(B*E)/pi = 0.99999249669706709988694199184339

Sqrt(B*F)/pi = 1.0004359804070626047872924366358

Sqrt(C*D)/pi = 0.99998979286235174661055696674446

Sqrt(C*E)/pi = 1.0000180250848698562144461553781

Sqrt(C*F)/pi = 1.0004615201163744427974657454632

Sqrt(D*E)/pi = 1.0000435541243760862784542220821

Sqrt(D*F)/pi = 1.0004870604776787765871125229875

Sqrt(E*F)/pi = 1.0005153067393101523150085623578

This process of multiplying two pi-lines and then taking the square root can be pursued methodically and results in approaching the value of pi exactly, except of course that we cannot produce a pi-line by this method that has an infinite number of decimal places.

12) Look again at the 1.2 series or the "Point Five" or "Eighteen Series":

PF=0.55, ES= (1/0.55)=1.81818181818181818181818181818182...

*1.2 = 2.18181818181818181818181818181818...

*1.2 = 2.61818181818181818181818181818181...

*1.2 = 3.14181818181818181818181818181818...

*1.2 = 3.77018181818181818181818181818181...

*1.2 = 4.52421818181818181818181818181818...

*1.2 = 5.42906181818181818181818181818181...

*1.2 = 6.51487418181818181818181818181818...

(sixfifths01 pg. 6)

The value of [sr(2)*3] divided by sr(5)+2 = 1.00155160626656770318654828804 = MN

Inverse = 0.99845079748576157160037849880869

4.2426406871192851464050661726291 / 4.2360679774997896964091736687313

Note that MQ / 1.001551606 = 0.99846609493127868861763485648117 = G

Inverse = 1.0015362615480968187413280761677

NEW pi line :

[sqrt(5)+2.2] / sqrt(2) = 3.136773748694594219681304368847 (pi*G) or G ***

(pi*G) * MN = 3.1416407864998738178455042012388 = (pi*MQ) or (pi*D)

and (pi*D) * MN = 3.1465153760315117097549686764016 = (pi*H)

and (pi*H)^2 = 9.9005590116027255345371092532438

= 9.9 * 1.0000564658184571247007181063883, or 9.9 * TN

sqrt(9.9) = (pi*J) = 3.1464265445104546409743605410398

J = 1.0015386752687805901365534786473

and G*J = 1.0000024100182653800808127097493

pi multipliers, such as G and J, are discoverable through mathematical calculations,

BUT NOT CONSTRUCTIBLE at this point.

(pi*MQ) = 3.1416407864998738178455042012388

MQ = 1.00001532118112944385403915398333

TN = 1.00005646581845712470071810638815

(10/3) = 3.33333333333333333333333333333333

(pi*MQ*TN) = (864/275) = 3.1418181818181818181818181818182

Try (10/3) - (Pi*MQ*TN), = 0.1915151515151515151515151515151...

You can do this on your calculator.

0.1915151515151515151515151515151...

* 2 = 0.383030303030303030303030303030...

* 2 = 0.766060606060606060606060606060...

* 2 = 1.532121212121212121212121212121...

/100,000 = 1.5321212121212121212121212121... * 10^(-5)

plus 1 = 1.00001532121212121212121212121212...

that / by 1.00001532118112944385403915398333

= 1.000000000030991293443952676684

And:

(secant 18)^4 * 9/11 = 1.0000564658184571247007181063881 (TN)

Inverse = 0.99994353736975150452258524923688

Plus 9 = 9.9999435373697515045225852492369

/by 10 = 0.99999435373697515045225852492369, and

0.99999435373697515045225852492369 * 0.99994353736975150452258524923688

= 0.99993789142552951643267541992405 and

0.99993789142552951643267541992405 * 1.22229123600033648574532213003

= 1.2222153212340807394416493082401, minus 0.2222 (1/5 + 1/50 + 1/500, + 1/5000)

= 1.0000153212340807394416493082401

/ by 1.00001532118112944385403915398333

= 1.000000000052950484323648939854

In the values observed here I see Evolutionary Proportion

But stuck on the initial set of pi lines for some time, then…

NEW INVENTORY (8/10/13): pi = 3.1415926535897932384626433832795

A-LT 1) 3.1406228624894574694952341031297 [ 2 + sqrt(5) ] – sqrt(6/5)

B-LT 2) 3.141320000468716979810539729062 [ sqrt(37) – 1] * (1/phi)

C-LT 3) 3.1414803893897418379555528189649 [ sqrt(pi*B* pi *D]

D-GT 1) 3.1416407864998738178455042012388 [ (9/5) + sqrt(9/5)] (pi*MQ)

E-GT 2) 3.14181818181818181818181818181821[(1/0.55*1.728] Pi*MQ*TN

F-GT 3) 3.1446055110296931442782343433718 [ sqrt(1/phi) * 4 ] (pi*Ho)

G-LT 4) 3.136773748694594219681304368847 [ sr(5) + 2.2] / sr(2)]

H-GT 4) 3.1465153760315117097549686764014

LT = less than pi GT = greater than pi

Then, "new" inventory of pi lines: LT = Less than pi, GT = Greater than pi

A-LT 1) 3.1406228624894574694952341031297 [ 2 + sqrt(5) ] – sqrt(6/5)

B-LT 2) 3.141320000468716979810539729062 [ sqrt(37) – 1] * (1/phi)

C-LT 3) 3.1414803893897418379555528189649 [ sqrt(pi*B* pi *D]

D-GT 1) 3.1416407864998738178455042012388 [ (9/5) + sqrt(9/5)] (pi*MQ)

E-GT 2) 3.1418181818181818181818181818181[(1/0.55*1.728] Pi*MQ*TN

F-GT 3) 3.1446055110296931442782343433718 [ sqrt(1/phi) * 4 ] (pi*Ho)

G-LT 4) 3.136773748694594219681304368847 [ sr(5) + 2.2] / sr(2)]

H-GT 4) 3.1465153760315117097549686764014 [pi*G*MN*MN]

J- GT 5) 3.1464265445104546409743605410398 [sr(9.9)]

And the pi multipliers are:

A/pi= 0.99969130590523006826067955285487

B/pi= 0.99991321181606256081092289835142

C/pi= 0.99996426519525912439773056310645

D/pi= 1.0000153211811294438540391539833

E/pi= 1.0000717878647096007586587022098

F/pi= 1.0009590223087825259636982582862

G/pi = 0.99846609493127868861763485648117

H/pi = 1.0015669512201377987045118132328

J/pi = 1.0015386752687805901365534786473

Notice certain interesting proportional relationships:

MN = sqrt(18) / [(sqrt5) + 2] = 1.00155160626656770318654828804

MN * (pi*G) = (pi*D), and MN^2 * (pi*G) = (pi*H), and

(pi*H)^2 = 9.9005590116027255345371092532429

= 9.9 * 1.0000564658184571247007181063882

and (pi*E) / (pi*D) = 1.0000564658184571247007181063881

and 1.0000564658184571247007181063881 * (11/9)

1.22229123600033648574532213003 = (secant 18) ^4

Performed extensive experimentation with the relationships among these pi lines and multipliers,

and then onto path of discovery of more truly new pi lines, including (pi*V) and (pi*Q).

Then: expanded pi line list as follows:

Complete pi line list with “MX” added:

A-LT 1) 3.1406228624894574694952341031297 [ 2 + sqrt(5) ] – sqrt(6/5)]

B-LT 2) 3.141320000468716979810539729062 [ sqrt(37) – 1] * (1/phi)]

C-LT 3) 3.1414803893897418379555528189649 [ sqrt(pi*B* pi *D]

D-GT 1) 3.1416407864998738178455042012388 [ (9/5) + sqrt(9/5)] (pi*MQ)

E-GT 2) 3.1418181818181818181818181818181 [(1/0.55*1.728] Pi*MQ*TN

F-GT 3) 3.1446055110296931442782343433718 [ sqrt(1/phi) * 4 ] (pi*Ho)

G-LT 4) 3.136773748694594219681304368847 [ sr(5) + 2.2] / sr(2)]

H-GT 4) 3.1465153760315117097549686764014 [pi*G*MN*MN]

J-GT 5) 3.1464265445104546409743605410398 [sr(9.9)]

K-GT 6) 3.1561090448809076493016604787293 [(9.9) / (pi*G) ]

L-GT 7) 3.1562872571612667838672356476287 [(pi*H)^2/ (pi*G)]

MX-GT 8) 3.1564654795045281880219131572653 [ L^2 / K]

Latest list of multipliers:

A/pi = 0.99969130590523006826067955285487

B/pi = 0.99991321181606256081092289835142

C/pi = 0.99996426519525912439773056310645

D/pi = 1.0000153211811294438540391539833

E/pi = 1.0000717878647096007586587022098

F/pi = 1.0009590223087825259636982582862

G/pi = 0.99846609493127868861763485648117

H/pi = 1.0015669512201377987045118132328

J/pi = 1.0015386752687805901365534786473

K/pi = 1.0046207108596739982308236137524

L/pi = 1.0046774375903516681481339875293

MX/pi = 1.0047341675241506141769603599752

Notice how (pi*K), (pi*L) and (pi*MX) were generated.

Then added (pi*JX) and (pi*KX) and (pi*NX), as follows:

JX = pi * sqrt(J*MX) = pi * 1.0031351489901143320921712389552 =

KX = (pi*J) * sqrt(J/G) = pi * 1.0015374684077115664482215879286

NX = pi*sr(J*G) = pi * 1.0000012050084066674103367893903

pi *JX = 3.1514420146250458834693530842498

pi*KX = 3.1512640759198245358269325763168

pi*NX = 3.1415964392353511387409825201656

Extensive experimentation and analysis of proportional relationships of these

pi lines. Also noting that:

3.84 = pi * MQ * (secant 18)^4

or (pi*MQ) * 1.22229123600033648574532213003, same as: (pi*MQ*TN) * (11/9)

(pi*MQ*TN) = 3.1418181818181818181818181818181 = (pi*MT) also

3.6 = (pi*MT) * (55/48) or * 1.1458333333333333333333333333333

3.24 = (pi*MT) * (33/32) or * 1.03125

3.2 = (pi*MT) * (55/54) or * 1.0185185185185185185185185185185

Extensive examination of the appearance of (cosine 18) and (secant 18) in these pi line proportional values, their squares and their fourths [ (secant 18)^4 ] etc.

Exploring some interesting proportions:

Looking at (9/11) and sr(9/11) and value of (cos 18)^2

9/11 = 0.81818181818181818181818181818182

11/9 = 1.2222222222222222222222222222222

sr(9/11) = 0.90453403373329086794043620091019

fr(9/11) = 0.95106994155702916313183885617663

sr(11/9) = 1.1055415967851332830383109122236

fr(11/9) = 1.0514473818433014116410422830982

(cos 18) = 0.95105651629515357211643933337938

(sec 18) = 1.0514622242382672120513381696958

(cos 18)^2 = 0.90450849718747371205114670859141

(sec 18)^2 = 1.1055728090000841214363305325075

(cos 18)^4 = 0.81813562148434214006393338573926

(sec 18)^4 = 1.22229123600033648574532213003

(sec 18)^4 = (11/9) * TN, * 1.0000564658184571247007181063881

(sec 18)^4 * 9 = 11.00062112400302837170789917027

(cos 18^4) = (9/11) * NT, * 0.99994353736975150452258524923688

And:

(cos 18)^2 / sr(9/11) = 0.99997176828636092476191921350642 = sr(NT), [ 1/sr(TN)]

sec(18)^2 / sr(11/9) = 1.0000282325106912323850835900966 = sr(TN)

and: (sec 18)^4 = 1.22229123600033648574532213003

times (pi*MQ) [1.8 + sr(1.8)], * 3.1416407864998738178455042012388 = 3.84

3.84 / 1.8 = 2.1333333333333333333333333333333 = (32/15)

sr(3.84) = 1.9595917942265424785578272597647

sr(32/15) = 1.4605934866804429692185860874688

and: sr(3.84) / sr(32/15) = 1.3416407864998738178455042012388 [sr(1.8)]

ALL CONFIRMED, … and further…

sr(9/11) * 3.84 = 0.90453403373329086794043620091019 * 3.84

= 3.4734106895358369328912750114951 STUDY FOR / pi*D

= pi * 1.1056209612557141301794630236278 [* (cos 18)^2 ] = sr(TN)

* (cos 18)^2 = * 0.90450849718747371205114670859141

= 3.1417294829069666872519934562529

which = pi * 1.0000435541243760862784542220821 = pi * sr(D*E) !!!

And: 3.84 / pi*sr(D*E) = 1.2222567286241781729151021656737

which = (11/9) * sr(TN)

And… (secant 18)^4 = 1.22229123600033648574532213003

* (25/24) or * 1.0416666666666666666666666666667

= 1.2732200375003505059847105521145 = [4/ (pi*D) ]

Another proportion of interest:

Phi^2 = pi * (5/6) * MQ, or (pi*D) * (5/6)

Same proportion as Phi^2 * (6/5) = (pi*MQ)

Therefore if sqrt(5/6), which equals sqrt(0.83333333333333333333333333333333)

which equals: 0.912870929175276855761616304668 is a factor of the radius of a circle,

then RD = sqrt(5/6) * N, and RD^2 = (5/6) * N^2, and AC (area of circle)

= pi * (5/6) * N^2, which is the same as Phi^2 * (N^2/MQ) CONFIRMED

Tested many possible combinations of the pi-line list (A through J) for path to

circle area equal to a square area.

FROM HERE FORWARD, USING ONLY SINGLE-LETTER LABELS:

(pi*A) = 3.1406228624894574694952341031297 [ 2 + sqrt(5) ] – sqrt(6/5)]

(pi*B) = 3.141320000468716979810539729062 [ sqrt(37) – 1] * (1/phi)]

(pi*C) = 3.1414803893897418379555528189649 [ sqrt(pi*B* pi *D]

(pi*D) = 3.1416407864998738178455042012388 [ (9/5) + sqrt(9/5)] (pi*MQ)

(pi*E) = 3.1418181818181818181818181818181 [(1/0.55*1.728] Pi*MQ*TN

(pi*F) = 3.1446055110296931442782343433718 [ sqrt(1/phi) * 4 ] (pi*Ho)

(pi*G) = 3.136773748694594219681304368847 [ sr(5) + 2.2] / sr(2)]

(pi*H) = 3.1465153760315117097549686764014 [pi*G*MN*MN]

(pi*J) = 3.1464265445104546409743605410398 [sr(9.9)]

A/pi = 0.99969130590523006826067955285487

B/pi = 0.99991321181606256081092289835142

C/pi = 0.99996426519525912439773056310645

D/pi = 1.0000153211811294438540391539833

E/pi = 1.0000717878647096007586587022098

F/pi = 1.0009590223087825259636982582862

G/pi = 0.99846609493127868861763485648117

H/pi = 1.0015669512201377987045118132328

J/pi = 1.0015386752687805901365534786473

And, for any "generic" pi-line, name is "pi*M" or for second line: "pi*N"

Then, another interesting proportion: generic for every (pi*M):

. 4 . = sqrt(Phi) * F = . 4 . * . 1 .

pi*MQ D pi D

. 4 . = sqrt(Phi) * F = . 4 . * . 1 .

pi*J J pi J

. 4 . = sqrt(Phi) * F = . 4 . * . 1 .

pi*M M pi M for any multiplier M

AND:

pi * D * sr(Phi) = D and pi * D * sr(Phi) = 4*D

4 F F

pi * J * sr(Phi) = J and pi * J * sr(Phi) = 4*J

4 F F

pi * M * sr(Phi) = M and pi * M * sr(Phi) = 4*M for any multiplier M

4 F F

AND:

D * (sec 18)^4 * 25 = sr(Phi) amazing

F 24

J * (sec 18)^4 * 25 = sr(Phi) * J amazing

F 24 D

Inverse:

. F * 24 * 1 . = . D . or = . F * 24 * (cos 18)^4 .

J * 25 * (sec18)^4 J*sr(Phi) J * 25

Old Note: Fact kept in mind throughout research, often thought to be the path to equality of areas, is that the area of any square is (4/pi) times the area of its inner circle (inner circumference tangent to sides of the outer square).

Another pattern occurs because (4/pi)^2 or 16/pi^2 = Phi * F^2

= 1.6211389382774043431020714113556

= 1.6180339887498948482045868343656 * 1.001918964341353794493972680575

Phi*(F/D) is therefore actually Phi * F^2 / (F*D). If we take:

. 2 . * . 2 . = . 4 . * . 1 . our result = Phi * F^2/ (B*E)

pi*B pi*E pi pi * B*E

and generically . 2 . * . 2 . = . 4 . * . 1 . our result will be

pi*M pi*F pi pi * M* F

Phi * F^2/ (F*M) = Phi * (F/M)

Additional research included many experiments with a pi-multiplier "N" being included as a factor in the radius of the circle, but could not find means to construct such an N value as a factor of the radius of a circle, and also be able to construct the (pi*N) value as a line.

Another interesting proportional pattern: Note the apparent relationships between rational fractions and common trigonometric functions:

(55/54) = 1.0185185185185185185185185185185

* E = 10.185916357881301489208560855841 = 32/pi

* 3 = (55/18) = 3.0555555555555555555555555555556

* E = 3.0557749073643904467625682567523 = 9.6/pi

and 2.5 * 1.22229123600033648574532213003

= 3.0557280900008412143633053250749 = 9.6 / (pi*MQ)

55/72 = 0.76388888888888888888888888888889

* E = 0.76394372684109761169064206418807 = 2.4/pi

1 / [2 * cosine 36)^2] = 0.76393202250021030359082633126872

and D / [2 * (cosine 36)^2] = 0.76394372684109761169064206418804 = 2.4/pi

11/36 = 0.30555555555555555555555555555556

66/45 = 1.4666666666666666666666666666667

45/66 = 0.68181818181818181818181818181818

Experiment with (864/275) = (6/5) * (144 / 55)

There are several interesting proportions equal to (4/pi):

. 4 . = F * sr(Phi)

4/pi = 25*MQ*SE = 275*MQ*TN

24 216

Some new algorithms and equalities:

3.072 is also a pi-line, and… for any pi-line (pi*M),

(pi*M) = M * . 100 . therefore

3.072 D (pi*F)^4

New equality - 3.2 is also a pi-line:

. 3.2 . = 55 * MT where (pi*MT) is same as (pi*E) in pi-line list

pi*M 54 M (pi*MT) = 3.1418181818181818181818…

This value = (55/54) * (MT/M), because 3.2 = (pi*MT) * (55/54)

or = 3.14181818181818181818 * 1.0185185185185185185

and this value also = sqrt(Phi) * (F/M) * 0.8 as follows: [3.2 / (pi*M) ]

1.2720196495140689642524224617375 * (F/M) * 0.8 CONFIRMED

An Eight-sixty-four (864) Table:

3.1418181818181818181818181818181, 1.0000564658184571247007181063881

3.1416407864998738178455042012388, 1.22229123600033648574532213003, 3.84

3.072 = 0.88/90 * pi*MT

88/90 = 0.97777777777777777777777777777778

= 864/281.25 = 3.84 * (8/10) =34.56/ 11.25

SE * (8/10) = 0.977832988800269188596257704024 = (pi*F)^4/ 100

3.14181818 = 1 * pi*MT = [(10/8) * previous]

= 864/275 = 3.84 * (9/11) = 34.56/11

SE * (9/11) = 1.0000564658184571247007181063882

3.2 = (55/54) * pi*MT

(55/54) = 1.0185185185185185185185185185185

= 864/270 = 3.84 * (5/6) = 34.56/ 10.8

SE * (5/6) = 1.0185760300002804047877684416917

3.456 = (11/10) * pi*MT

= 864/250 = 3.84 * (9/10) = 34.56/ 10

SE * (9/10) = 1.100062112400302837170789917027

3.84 = (11/9) * pi*MT

= 864/225 = 3.84 * 1[9/9] = 34.56/ 9

SE * 1 = 1.22229123600033648574532213003

4.32 = (11/8) * pi*MT

= 864/200 = 3.84 * (9/8) = 34.56/ 8

SE * (9/8) = 1.3750776405003785464634873962838

4.9371428571428571428571428571427 = (11/7) * pMT

1.5714285714285714285714285714286 * 3.1418181818181818181818181818181

= 864/175 = 3.84 * (9/7) = 34.56/ 7

SE * (9/7) = 1.5715173034290040531011284528957

5.76 = (11/6) * pi*MT

= 864/150 = 3.84 * (9/6) = 34.56/ 6

SE * (9/6) = 1.833436854000504728617983195045

= (11/6) * 1.0000564658184571247007181063882

6.912 = (11/5) * pi*MT

= 864/125 = 3.84 * (9/5) = 34.56/ 5

SE * (9/5) [1.8] = 2.200124224800605674341579834054

= 2.2 * 1.0000564658184571247007181063882

8.64 = (11/4) * pi*MT

= 864/100 = 3.84 * (9/4) = 34.56/ 4

SE * (9/4) [2.25] = 2.7501552810007570929269747925675

= 2.75 * 1.0000564658184571247007181063882

11.52 = (11/3) * pi*MT

= 864/75 = 3.84 * (9/3) = 34.56/ 3

SE * (9/3) [3] =3.66687370800100945723596639009

= (33/9) * 1.0000564658184571247007181063882

17.28 = (11/2) * pi*MT

= 864/50 = 3.84 * (9/2) = 34.56/ 2

SE * (9/2) = 5.500310562001514185853949585135

= 5.5 * 1.0000564658184571247007181063882

A key equality in the path to the solution:

(pi*MT) * (10/9) = (192/55) = 3.49090909090909090909090909…

and therefore for any "M" in (pi*M),

(pi*M) * (10/9) = (192/55) * (M/MT) [ for all (pi*M) ]

Next, a new and key pi-line on the path to the solution:

(40/9) = 4.44444444444444444444444444444444444…

that times sqrt(0.5) = 3.1426968052735445528926416093549 = (pi*V)

and V = 1.0003514623967845217279991011186

and V^2 = 1.0007030483193853969765872909603

Note also that (40/9) * (D/F)^2 = 4.4360679774997896964091736687314

(D/F) = 0.9990572030356683643723210527954

D/F)^2 = 0.99811529493745268169206407546457

and 4.4360679774997896964091736687314 = [ sqrt(5) + 2.2 ]

Looking more closely at (pi*V) = 3.1426968052735445528926416093549

(pi*V)^2 = 9.8765432098765432098765432098766, where digital values are

the decimal number system in reverse: 9. 8 7 6 5 4 3 2 0 98765432 0987654320… etc

and the inverse [ 1/ (pi*V)^2 = 0.10125 AND THE POINT HERE IS THAT THIS

DOES NOT APPEAR TO BE MEANINGLESS "NUMEROLOGY" BUT IS SUSPICIOUS

AT LEAST. Also suspicious in light of other equalities:

0.10125, * 2 = 0.2025, * 2 = 0.405, * 2 = 0.81, * 2 = 1.62

and 1.62 * V^2 = (4/pi)^2 = 1.6211389382774043431020714113556

and 4 / (pi*V) = 1.2727922061357855439215198517887 = sqrt(1.62)

and Phi = 1.62 * 0.99878641280857706679295483602817 or 1.62 * (V/H)

THEREFORE…

ARE YOU BEGINNING TO SEE WHAT I SEE? THIS IS THE MEANING OF PROPORTION. WE SEE IT WHEN WE SEE THE VINES TWINING, THE PATTERNS OF LEAF NODES ON A STEM AND THE SUNFLOWER SEEDS IN THE POD. THE SPIRAL CURVES INSIDE THE NAUTILUS, THE GOLDEN SECTION IN ALL LIVING THINGS, AND WHEN WE LOOK AT THE DIGITAL OUTPUT OF THE MANDELBROT SET AND WE SEE THE FAMILIAR ORGANIC SHAPES OF FROST AND NEEDLES AND PAISLEY PATTERNS AND THE BRANCHES OF TREES AND RIVERS -- ALL THIS WE SEE IN THE GEOMETRIC SHAPES, BUT HERE I ENDEAVOR TO SHOW THAT WE CAN SEE THIS SAME PATTERN OF PROPORTION IN NUMBERS. THE REALITY OF PHYSICS AND THE NATURAL WORLD, THE REAL, PHYSICAL UNIVERSE IS THAT OUR EYES DETECT A NARROW SLICE OF THE ELECTROMAGNETIC SPECTRUM AND WE NAME THAT PERCEPTION "GREEN." OUR EARS DETECT A NARROW SLICE OF THE VIBRATIONAL SPECTRUM AND WE NAME THAT PERCEPTION "HIGH C" OR "MEADOWLARK." SO WHAT I AM TRYING TO TEACH THE WORLD IS THAT WHEN WE DETECT A PARTICULAR PROPORTION WE NAME THAT PERCEPTION "FIVE." MATHEMATICS IS A LANGUAGE, A VOCABULARY TO DESCRIBE PROPORTIONS, AND COUNTING AND MEASURING PROPORTIONS. I AM SAYING THAT THIS IS WHAT MATHEMATICS IS. AND THAT MEANS MATHEMATICS IS A CULTURAL INVENTION, A PRODUCT OF THE HUMAN INTELLECT, NOT A PRODUCT OF THE COSMOS. PROPORTION IS NOT A PRODUCT OF THE COSMOS. PROPORTION IS THE ORIGIN OF THE COSMOS, AND OUR MATHEMATICS IS OUR LANGUAGE FOR TALKING ABOUT PROPORTION. ANOTHER DIFFERENT LANGUAGE FOR TALKING ABOUT PROPORTION IS POSSIBLE, BUT PROPORTION IS THE TRULY UNIVERSAL LANGUAGE BECAUSE ALL PROPORTIONS ARE THE SAME FOR ALL PERCEIVING INTELLECTS. ANOTHER SPECIES CAN HAVE ANOTHER WORD FOR "FIVE" BUT CANNOT HAVE ANY OTHER PERCEPTION FOR FIVE EXCEPT THE FIVE THAT IS FIVE EVERYWHERE WITHIN THE ONE BIG SETTING THAT WE CALL THE UNIVERSE.

Continuing…

sqrt(162) = 9 * sqrt(2) = 12.727922061357855439215198517887

/4 = 3.1819805153394638598037996294718 let = (A)

and pi * 1.0125 = 3.1808625617596656539434264255705 let = (B)

and A/B = 1.0003514623967845217279991011186, = V

OR: V = sqrt(10.125) / [ pi * 1.0125], sqrt(10.125) = V * [pi* 1.0125]

AND sqrt(10.125) = pi * 1.0125

ARE YOU SURE THIS IS JUST "NUMEROLOGY"?

(0.9*pi) = 2.8274333882308139146163790449516 (9/10)

= sr(8) * 0.99964866108563240557857322276366

inverse of V: 1.0003514623967845217279991011186

and (pi*V) = sr(8) * (10/9)

And: (108 / 11) = pi * MQ*TN * 3.125

9.818181818181818 = 3.1418181818181818 * 3.125

And: (pi*M) * 0.9 = sqrt(8) * (M / V) for all M

ANOTHER PATTERN:

169/54 = 3.1296296296296296296296296296296

170/54 = 3.1481481481481481481481481481481

1695 / 540 = 3.1388888888888888888888888888889

16955 / 5400 = 3.1398148148148148148148148148148

169557 / 54000 = 3.1399444444444444444444444444444

169566 / 54000 = 3.1401111111111111111111111111111

169568 / 54000 = 3.1401481481481481481481481481481

16957 / 5400 = 3.1401851851851851851851851851852

16965 / 5400 = 3.1416666666666666666666666666667

169645 / 54000 = 3.1415740740740740740740740740741

1697/540 = 3.1425925925925925925925925925926

Also: 1/ 0.81 = 1.234567901 * (cos 36) = (V/F)^2

Also: (1024 / 33) = 31.0303030303030303030303030303030

= pi^3 * [V^2 * MT] or 31.006276680299820175476315067101

* 1.000774886654432634086308544033 = (1024 / 33)

Initial notes for a table of equalities: [ sr = sqrt = square root of]

pi*M * sr(cos 36) = sr(8) * . M . and pi*M * 0.9 = sr(8) * . M .

F V

pi*M * (10/9) = 192 * M . and pi*M * (10/9) * (cos 36) = VARIES

55 * MT

A) pi*H * (10/9) * (cos 36) = sr(8)

B) pi*G * (10/9) * (cos 36) = sr(8) * . V .

C) pi*M * (10/9) * (cos 36) = sr(8) * . M .

New: pi*M * (cos 36) = . M . * sr(Phi) * 2

pi*M * sr(8) = . M . * 80 pi*M * (11/9) = 3.84 * . M .

V 9 MT

pi*M * sr(2) = . M . * 40 .

V 9

Expanding a table of equalities: [ sr = sqrt = square root of]

pi*M * sr(cos 36) = sr(8) * . M . and pi*M * 0.9 = sr(8) * . M .

F V

SQD: (pi*M)^2 * (cos 36) = 8 * M^2 and (pi*M)^2 * 0.81 = 8 * M^2

F^2 V^2

pi*M * (10/9) = 192 * M . and pi*M * (10/9) * (cos 36) = VARIES

55 * MT

SQD: (pi*M)^2 * (10/9)^2 = (192 * M)^2

(55 * MT)^2

A) pi*H * (10/9) * (cos 36) = sr(8), (pi*H)^2 * (10/9)^2 * (cos 36)^2 = 8

[ (10/9)^2 * (cos 36)^2 = (cos 36) * (F/V)^2

B) pi*G * (10/9) * (cos 36) = sr(8) * . V . , SQD = 8 * (V/G)^2

C) pi*M * (10/9) * (cos 36) = sr(8) * . M . , SQD = 8 * (M/H)^2

New: pi*M * (cos 36) = . M . * sr(Phi) * 2

pi*M * sr(8) = . M . * 80 pi*M * (11/9) = 3.84 * . M .

V 9 MT

SQD: (pi*M)^2 * 8 = (M*80)^2 (pi*M)^2 * (11/9)^2 = (3.84)^2 * . M^2 .

(V * 9)^2 MT^2

pi*M * sr(2) = . M . * 40 . , (pi*M)^2 * 2 = (M * 40)^2

V 9 (V * 9)^2

Expansion of new equalities:

A) sr(8) = 2 * sr(Phi) and 8 = 4 * Phi

sr(cos 36) (cos 36)

B) (pi*V) * (pi*MT) = sr(8) * (192/55) = 9.8737819627503363407245176381186

3.4909090909090909090909090909091 * 2.8284271247461900976033774484194

(pi*D) * (pi*MT) = sr(8) * (192/55) * . D . and this is GENERIC ALGORITHM

(pi*M) * (pi*MT) = sr(8) * (192/55) * . M . AND

(pi*M) * (pi*V) = sr(8) * (192/55) * . M .

sr(8) denominator series:

sr(8)/V = 0.9 * pi COULD BE IN AC

sr(8)/F = sr(cos 36) * pi

sr(8)/H = (cos 36) * 10/9 * pi

sr(8)/D = 0.9 * (V/D) * pi

= 2.8283837905658312555117435832181

= 0.90030252245908817867181052349698 * pi

= 0.9 * 1.00033613606565353185756724833 = 0.9 * (V/D)

sr(8)/MT = 0.9 * (V/MT) * pi

= 2.8282240925776636989105723895062

= 0.90025168901065078338070462767978 * pi

= 0.9 * 1.0002796544562786482007829196442 = 0.9 * (V/MT)

sr(8)/G = 0.9 * (V/G) * pi = 2.8327723285795317134639799997497

(V/G) = 1.0018882638830471224770463536466

* 0.9 = 0.90169943749474241022934171828192

Discovery of (pi*Q):

. sr(Phi)* sr(8)* 48. = 172.69511423499525813707784802793

55 55

= 3.1399111679090046934014154186896 = (pi*Q)

which also = (pi*V) * (pi*MT)

(pi*F)

And: (pi*Q) * sr(sec 36) = (192/55) Q * sr(sec 36) * 0.9 = MT

And note that: (10/9) * (MT/Q) = sr (secant 36) [new equality]

Therefore: (pi*M) * sr(sec 36) [ 1.1117859405028423439840960957951 ]

= (pi*M) * (10/9) * (MT/Q) = (192 / 55) * (M/Q) [FOR ALL M ]

OR: (pi*M) * sr(se 36) = (192 / 55) * (M/Q) [FOR ALL M ]

Also, note three-way equality:

pi * Q * (V/F) = pi * Q * (Q/MT) = 192 * sr(8) .

55 * (pi*H)

= 3.1380053115149475843967744666485 when this value = R^2

Same as: (pi*Q) * sr(cos 36) = sr(8) * Q , [ * 10] = sr(8) * Q * sr(sec 36)

F 9 H

= 3.1380053115149475843967744666485

I have many more pages of interesting proportional values, all of which played a role in leading me to the solution described in SOLITU G: USING THE 5 PI LINES THAT ENABLE CONSTRUCTION OF LINE A, MINUS LINE B, = pi exactly * 0.1118.

THE UNIFICATION CONSTRUCTION: The best evidence that "Proportion is Everything" and proportion is the fundamental force of Nature that is the origin of the shapes of matter in the universe and not a product of other forces in the universe (see Aristotle's OM):

QUICK VERIFICATION OF THE UNIFICATION CONSTRUCTION:

The validity of the Unification Construction can be completed in a few minutes using a scientific calculator, either a hand-held calculator or a desktop computer calculator in scientific view. I am using my Casio fx-115MS that allows saving six values in memory (A, B, C, D, E, F)

1) PL[8] = 3.1416407864998738178455042012388; (pi*D)

2) PL[11] = 3.1446055110296931442782343433718; (pi*F)

3) PL[9] = 3.1418181818181818181818181818181; (pi*E)

4) PL[10] = 3.1426968052735445528926416093549; (pi*V)

5) PL[3] = 3.1399111679090046934014154186896; (pi*Q)

6) The inverse of HG: (1 / 0.1118) = 8.9445438282647584973166368515206

or (1 / 1.118) = 0.89445438282647584973166368515206

same as sqrt(0.8) * 1.0000304013863102398967681881625

"Construct" and save the pi-line values using the hand-held calculator, press the following keys, including the parentheses. Press keys indicated to the vertical bar "|" then press the save key or keys. I saved to the letters shown below but any order is fine.

1) 1.8, square root, + sqrt(1.8) = | pi-line (pi*D) press save key, save to "C"

2) sine 18, times 2, sqrt, * 4 = | pi-line (pi*F) press save key, save to "A"

3) 0.55, press (1/X) key [inverse], times 1.44, times 1.2 = | pi-line (pi*E) save to "D"

4) 40 / 9 = , that times sqrt(0.5) = | pi-line (pi*V) press save key, save to "F"

5) (pi*E) [D key] times (pi*V) [F key] / (pi*F) [A key] = | (pi*Q) save to "B"

6) (1/0.1118) There are several ways to construct this number, but the procedure

shown below seems most convenient: [HG = 0.1118]

0.9 * 0.8 = 0.72, + 4 = 4.72

/ 5 = 0.944, + 8 = 8.944

/ 8 = 1.118, inverse = (1/1.118) = 0.894454382826475

press save key, save to "E" and THEN PROCEED:

Line A: (pi*V)^2 / (pi*E) / sqrt(cos 36)

= 3.49498323774898999309129431119694 (Line A) ***

[ / by sqrt(cos 36) is the same as times sqrt(sec 36)]

minus Line B: - [ (pi*V)^2 / (pi*D) ] is the same as

minus 3.14375317901321112588817420275095 (minus Line B) ***

That is: 3.494983238 minus 3.143753179

= 0.351230058735778867203120108445054 = (Line C) or [ = pi * HG exactly] ***

times 5 = 1.75615029367889433601560054222527

times 1/1.118 = 1.57079632708308974598890925064872

same as times 0.89445438282647584973166368515206 ***

times 2 = pi exactly, 3.141592654 16617949197781850129744 *** to 9th place here

see important note below on calculator precision!

OR, 0.351230058735778867203120108445054 times 10, / pi

= 1.118000000 20511883699932630279168 good to 9th place.

Note that to multiply by 5 can be done by adding the line 5 times or use the

SRT method to multiplie by the ratio sqrt(5) and then again by sqrt(5).

CALCULATIONS FOR THE CONSTRUCTION OF PROPORTIONS ONLY (NOT "pi-lines"):

440,000 . = our Line A

139,968 * sr(cos 36)

= . 440,000 .

139,968 * 0.899453719973933636130613791812128

= . 440,000 .

125894.73827731154318192975121236

= 3.49498323774898999309129431119871, our Line A

[inverse = 0.286124405175708052686203980028091]

. 1,000 . = our Line B

486 * (cos 36)^2

= . 1,000 .

486 * 0.65450849718747371205114670859141

= . 1,000 .

318.091129633112224056857300375425

= 3.14375317901321112588817420275195, our Line B

[inverse = 0.318091129633112224056857300375425]

AND: common denominator is: 139,968 * (cos 36)^2

sqrt(cos 36) * (cos 36) * 440,000 = our Line A

139,968 * (cos 36)^2

= 0.727673345112677404061330919854849 * 440,000

91610.2453343363205283749025081224

= 320176.271849578057786985604736133

91610.2453343363205283749025081224

= 3.49498323774898999309129431119871 CONFIRMED A

minus . 288 * 1,000 . our Line B

91610.2453343363205283749025081224

= 3.14375317901321112588817420275203 CONFIRMED B

= 0.351230058735778867203120108445968 = (A minus B)

= pi * 0.1118000000 20511883699932630279 476 10th place, THE SOLUTION

Same as:

320176.271849578057786985604736133 - 288,000

or: 32176.2718495780577869856047361

/ by 91610.2453343363205283749025081224

= 0.351230058735778867203120108446405 CONFIRMED

minor differences in extended digits due to calculator limitations

= pi * 0.1118000000 20511883699932630279 615

and note proportional value for 139,968 * (cos 36)^2

= 6 * 9 * 1.44 * 1.8 = 139.968 * (cos 36)^2

as 54 * 2.592 or 8.64 * 16.2 = 139.968, and 139.968

times (cos 36)^2 = 91.6102453343363205283749025081224

CONFIRMED, end of calculation by proportions only (not "pi-lines")

Important note on the precision of the constructions and calculations:

I hope you have an opportunity to test for the infinite precision of this Unification Construction of pi exactly. Your hand-held or computer calculator is probably accurately precise only to the 9th decimal place. As one uses a more precise electronic math processor, the number of zero digits to the right of the decimal point will increase. Only Nature has a math processor of infinite precision. What value should we accept as "pi-exactly"? Due to pi-mania of some people, including some mathematicians, pi has been calculated, using high-precision computers, to 50 decimal places, then 100, then 1,000 and far more than a million decimal places. Those calculations did not accomplish anything useful. The precision of calculation is meaningful in the real, physical universe only to the 12th or 13th decimal place, because 600 picometers, or 600 times one-trillionth of a meter, which equals 0.000 000 000 600 of a meter, IS THE MAXIMUM WIDTH OF AN ATOM. That means that if we had a metal rod of a measured length that was 1.000 000 000 600 meters, then we could not change any of the decimal digits following the 6 unless we added another atom of length, which would then make the measurement 1.000 000 001 200 meters. It is clear that we cannot change any of the digits following the six in the ending 600 because that would mean we added less than an atom of length to the rod, which we cannot do. Any process that results in precision to the 12th decimal place has reached not only our technical capacity to measure, but Nature's limit of the smallest possible particle of matter. There may be smaller particles, but they cannot be added to or subtracted from a physical object to change that object's physical size.

Hope you are at least suspicious about the signs shown here that "proportion is everything" and you will explore this theory further. It needs to be taken seriously and "ruled out" by rigorous examination and experimentation and not simply dismissed by arbitrary doctrine.