pi-Profiling Concepts Post December 2011 using [ 16/pi ] denoted f1 ( updated August 10th 2018. 7:18 AM. ) . Author: Kevin John Trinder, independent researcher . Please note i am dyslexic and use of the periods is to keep me focused . We began this paper on October 30 th 2013. update have fallen behind due to illness . . Introduction: Mathematical Poem on Circle: Plane Figure ( circle ) PFC . Circle: Definition of plane-figure circle ( PFC ) and its circumference ( cir ) . In Geometry all lines and all points have no width, breadth or depth . Our PFC’s circumference when drawn on a perfectly flat plane, is an imaginary perfect curve of infinitely many imaginary points . being of no width, breadth or depth . . Our PFC’s centre is also an imaginary point being of no width, breadth or depth . . Each of the infinitely many imaginary points of our PFC’s circumference is equidistant from our PFC’s imaginary centre point . . Lines may be drawn tangent to our PFC’s circumference but not reside on our PFC’s circumference . . The surface area within our PFC does not encroach onto our PFC’s circumference . . At no time should we imply that numerical concepts or numerical outcomes reside on the circumference of our PFC . . When we assign a numerical value in general to our PFC’s diameter D we change the dynamics of our PFC's perfectly . curved circumference to a pi-Profiling Perimeter ( P ) . pi dose not reside on our PFC’s circumference, it is a pi-Profiling Perimeter P value, residing just below our PFC's circumference . . The agreed and accepted value of pi extracted from prime numbers is a truncated constant meaning that there is a time lapse from . observing the largest known prime number to the next yet to be found progressive largest prime number . . When the diameter D of our pi-Profiling Perimeter P is positive integer one our pi-Profiling Perimeter P is pi . . When the diameter D of our pi-Profiling Perimeter P is the inverse of pi our . pi-Profiling Perimeter P is [ pi * (1/pi) ] is notionally positive integer one . . When we consider the diameter of our PFC to be a straight line of infinitely many imaginary points being of no width, breadth or . depth we can use our pair of compasses and unmarked rule to show the imaginary point along our diameter D for . our Golden Section Ratio ( GSR ) . . From our pi-Profiling Perimeters P diameter D and radius R we can give our GSR value from right angle triangle D : R and the first . and second cuts with our pair of compasses . . Kevin John Trinder, began October 30th 2013. updated May 26, 2016. Page of 1 25
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pi-Profiling Concepts Post December 2011 using [ 16/pi ] denoted f1 ( updated August 10th 2018. 7:18 AM. )
.
Author: Kevin John Trinder, independent researcher .
Please note i am dyslexic and use of the periods is to keep me focused .
We began this paper on October 30th 2013. update have fallen behind due to illness . .
Introduction: Mathematical Poem on Circle: Plane Figure ( circle ) PFC .
Circle: Definition of plane-figure circle ( PFC ) and its circumference ( cir ) .
In Geometry all lines and all points have no width, breadth or depth .
Our PFC’s circumference when drawn on a perfectly flat plane, is an imaginary perfect curve of infinitely many imaginary points .
being of no width, breadth or depth . .
Our PFC’s centre is also an imaginary point being of no width, breadth or depth . .
Each of the infinitely many imaginary points of our PFC’s circumference is equidistant from our PFC’s imaginary centre point . .
Lines may be drawn tangent to our PFC’s circumference but not reside on our PFC’s circumference . .
The surface area within our PFC does not encroach onto our PFC’s circumference . .
At no time should we imply that numerical concepts or numerical outcomes reside on the circumference of our PFC . .
When we assign a numerical value in general to our PFC’s diameter D we change the dynamics of our PFC's perfectly .
curved circumference to a pi-Profiling Perimeter ( P ) .
pi dose not reside on our PFC’s circumference, it is a pi-Profiling Perimeter P value, residing just below our PFC's circumference . .
The agreed and accepted value of pi extracted from prime numbers is a truncated constant meaning that there is a time lapse from .
observing the largest known prime number to the next yet to be found progressive largest prime number . .
When the diameter D of our pi-Profiling Perimeter P is positive integer one our pi-Profiling Perimeter P is pi . .
When the diameter D of our pi-Profiling Perimeter P is the inverse of pi our .
pi-Profiling Perimeter P is [ pi * (1/pi) ] is notionally positive integer one . .
When we consider the diameter of our PFC to be a straight line of infinitely many imaginary points being of no width, breadth or .
depth we can use our pair of compasses and unmarked rule to show the imaginary point along our diameter D for .
our Golden Section Ratio ( GSR ) . .
From our pi-Profiling Perimeters P diameter D and radius R we can give our GSR value from right angle triangle D : R and the first .
and second cuts with our pair of compasses . .
Kevin John Trinder, began October 30th 2013. updated May 26, 2016.
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Abstract .
To find the word seeds of notion to describe the numerical environment within and about our .
pi-Profiling Perimeter P observed when we assign a numerical value in general to .
our Plane Figure ( circles ) diameter using an electronic spreadsheet or computer program . .
We begin . .
pi-Profiling Formula Facilitators ( f ) are denoted { f1, f2, f3, f4, f5, f6 . . . } .
pi-Profiling Environment Formula Facilitators ( e ) are denoted { e1, e2, e3, e4, e5, e6, e7 . . . } . .
Known Formula Facilitators ( KF ) are agreed and accepted Number Theory constants and Mensuration aid values .
for example: pi itself and our Golden Section Ratio ( GSR ), the sqrt 2, the sqrt 3, the sqrt 5, the sqrt 6 . .
From about 1989, my dyslexic mind began thinking about and asking, why its it that when we .
divide a numerical outcome in general by pi that the quotient may considered notionally to be .
the radius R squared R^2 of our pi-Profiling Perimeter P ? .
Not so long after the above question came to mind, i was thinking about dividing the square root .
of all sorts of numerical outcomes and VOI, into our pi-Profiling Perimeter P .
The day arrived when i divided the square root of 2/4, 0.5, into our pi-Profiling Perimeters 1P value .
of 2pi, giving us the quotient of 8.88576587631673 denoted 1Psi
1Psi being the number of √D/4 increments about our pi-Profiling Perimeter 1P . .
for a pi declaration of 3.14159265358979 denoted pi14, being pi to14 decimal places .
0.636009824757034 √(1PDi) 0.750765630241671 1Pe3 quotient =~ 0.847148296536035 √(1PDe) our companion square root value to √(1PDi) .
7.99233517227052 1Psi, number of √(Di) increments (s) about our pi-Profiling Perimeter 1P 0.750765630241671 1Pe3 quotient =~ 10.6455794595949 1Psic number of √(1PDe) increments about 1Pc .
12.3861189839612 kSV our companion sphere volume value to 1PSV .
3.23606797749979 ( D*2 ) our pi-Profiling Perimeters diameter 1PD times two 0.635400461539407 1Pe5 product =~ 2.05619908647626 1PA our pi-Profiling Perimeters area 1PA .
2.05619908647626 1PA our pi-Profiling Perimeters area 1PA 0.317700230769704 1Pe1 quotient =~ 6.47213595499958 1PAc our companion area value to area 1PA
As we add more facets of geometry to our electronic spreadsheet our pi-Profiling data becomes more interesting .
Authors note: March 22, 2016. ( updated April 6th 2016. PM ) .
Science and the notion of 1.37596919694205 inverse value being 0.7267604552648 .
i have noticed recently that you are using Quote: 2-(4/pi) =~ 0.726760455264. End-quote .
and Quote: 1-(2/pi) =~ 0.36338022763242 End-quote .
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OK, lets consider the notion of one Radian and our pi-Profiling Perimeters numerical environment . .
The following internet searches may not be related: Physics, Particle Physics, Nuclear Physics .
notion of quantum random walks or perhaps you are considering EPR Paradox – Bell’s Inequality .
Perimeter logic or the notion of electronics and the numerical outcome of 0.726760455264837 .
inverse value being 1.37596919694205 or Kepler’s Equation’s and the notion of .
Authors note: April 1, 2016. Quote: Keywords, KM3NeT; Neutrino telescope; Trigger End-quote Quote: The maximum event time for KM3NeT is 8300 ns End-quote
.
. we observe 57.2957795130822 * 10 =~ 572.957795130822. being ( 1Psi ) .
we observe [(572.957795130822 / 4pi)^2] *4 =~ 8315.44562629427 being our diameter 1PD .
? we may be observing a base10 anomaly ? . .
Authors notes: April 3, 2016. ( updated June 6, 2016 ) .
OK, lets consider the notion of our pi-Profiling Perimeters P and the inverse of its diameter 1PD. .
My pi-Profiling Formula for the inverse of our diameter, 1/1PD is: .
1/PD =~ f16 / (Psi)^2 . .
where f16 is (2pi)^2 being 39.4784176043574 .
Kevin John Trinder, April 3, 2016.
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Authors notes: February 14th 2016. ( updated April 7, 2016 PM) .
We have observed that approximation inverse values for our notional fine-structure ( α ) outcomes are found .
between 1Psi =~ 73.5427 and Ps =~ 73.553 via pi-Profiling Formula [( Ps / 4pi )^2] * 4 =~ approx. 1 / α
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Authors note: February 18th 2016. updated August 2018. . .
When we use the number six, or we have six of anything . >< .
or when we use √2, √3 and √6 we must be aware that 4 * ( √ pi ) being 7.0898154036221
may be written as: {(√pi/3)*(√8)}* [√6] =~ 4*√pi . 1.02332670794649 being √ ( pi / 3 ) 2.82842712474619 √8 product =~ 2.89440501823307 being [ √ ( pi / 3 ] * [ √8 ] .
2.89440501823307 being [ √ ( pi / 3 ] * [ √8 ] 2.44948974278318 being √6 also being (√2) * (√3) product =~ 7.08981540362206 being 4 * ( √ pi )
my concern is in reference to the notion of Hadrons, Mesons ( 1 quark plus 1 anti-quark ) and the quotients arrived at by division using √2 ,√3 and √6
.
Authors notes: February 20th 2016.
when we use number six, or we have six of anything containing .
or dividing by number 6 .
. >< .
6, √6, (1/pi) and the notion of Quote: C-parameter and coupling constant End-quote . .
Authors notes: February 20th 2016.
Quote: Particle momentum in the Centre of Mass
Quoting paper: Properties of C-parameters and coupling constant
Contributions to C-parameter n=~2; A; 2.4317 End-quote. . .
Ok, i am know going back to October 29th 2002 when i observed the following pi-Profiling outcome of : 2.43170840741611 .
i posted the pi-Profiling Formula for this outcome 2.43170840741611. to my web site at that time. . .
We observe 4*pi =~ 12.566370614359. =~ f4 . when Psi =~ 12.566370614359. we observe wDi =~ 1 and 1^2 =~ 1, our 1PDi value . when Psi =~ -12.566370614359. we observe wDi =~ -1 and -1^2 =~ 1, our 1PDi value . We can observe wDi as ( -pi / pi ) =~ -1 and (-1)^2 =~ 1 . .
When 1Psi =~ 1 we observe wDi =~ 1/4pi =~ 0.0795774715459 and (1/4pi)^2 =~ 0.0063325739776 our 1PDi value .
When 1Psi =~ -1, we observe wDi =~ -0.079577471545947 and ( -0.079577471545947 )^2 =~ 0.006332573977646 our 1PDi value
.
n.b. We observe that for 1Psi =~ 1 and for 1Ps =~ -1 our perimeter P and its wDi value .
are equal to each other being 0.079577471545947 =~ 1/4pi being f9 .
We observe pi/3 =~ 1.047197551196 =~ f7 . when 1Psi =~ -12 we observe wDi =~ -0.95492965855137 =~ 1/( -1.047197551196 ) . we observe -0.95492965855137^2 =~ 0.91189065278104 =~ ( 9 / pi^2 ) .
we observe -0.95492965855137 / 0.91189065278104 =~ pi/3 =~ 1.047197551196 . when 1Psi =~ -1.047197551196 we observe wDi =~ -0.08333333333333 =~ 1/-12 . we observe -0.08333333333333^2 =~ 0.006944444444444 =~ our perimeters 1PD/4. .
we observe 0.0069444444444444 * 4 =~ 1/36
. we observe 0.0833333333333333 =~ 1/12
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We observe pi divided by the square root of 8 =~ 1.110720734539 =~ f101 . when 1Psi =~ ( f101 ) we observe wDi =~ 0.0883883476483 . we observe 0.0883883476483^2 =~ 0.0078125 =~ our 1PDi value
. we observe pi divided by 3 =~ 1.047197551196 =~ f7 . we observe the square root of 1.125 =~ 1.0606601717798 . we observe (f101) / (f7) =~ 1.0606601717798 being f109 ( observed January 2012 )
.
When 1Psi =~ {1, 2, 3, 4, 5, 6…} . we observe wDi =~ 1* (1/4pi), 2* (1/4pi), 3* (1/4pi), 4* (1/4pi), 5* (1/4pi), 6* (1/4pi), … . we observe: f9 being 1/4pi =~ 0.079577471545947 . and 0.079577471545947 * 10 =~ [1*(1/4pi)] + [2*(1/4pi)] + [3*(1/4pi)] + [4*(1/4pi)]
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When 1Psi =~ GT 2015 November 23rd =~ 6.6743257318364124595179244522346e-11 . we observe wDi =~ 0.53112596601359 . [( 0.53112596601359. )^2] * 4 =~ 2/( f6 ) =~ 1.12837916709551 being f8 and ( f8 )^2 =~ 4/pi .
1/{[(0.53112596601359)^2]*2} =~ the square root of pi =~ 1.7724538509 being f6 . .
GT 2015 November 19th = 6.6743257318364124595179244522346e-11
On January 16th 2015 i wrote an Elegant pi-Profiling Loop Formula number one (EpPLF1) .
enabling us to observe our numerical outcomes of 55?????? with respect to the .
notion of our fine-structure constant. e.g. prime number 73 FSD 55?????? . .
73 FSD 5524602095245869 ( FSD: full stop delimiter ) .
73.5524602095245869 1Psi number of wDi increments about our pi-Profiling Perimeters 1P 0.0795774715459477 f9 being (1/4pi) product =~ 5.853118809457890857 being our wDi value . 5.853118809457890857 being our wDi value squared =~ 34.25899979762975765 our pi-Profiling Perimeters 1PD/4 value denoted 1PDi .
137.035999190519030630593328668 inverse of my fine-structure constant value inverse =~ 0.0072973525636115183384116343457 being my notional value for the fine-structure constant:
.
.
Today is January 28th 2016. ( updated April 6, 2016 ) Numerical outcomes .
observed from pi-Profiling when our 1Psi value of interest ( VOI ) is positive integer 13 . .
pi-Profiling the numerical environment within and about our pi-Profiling Perimeter P when our 1Psi value, being the number of wDi increments about 1P
is positive integer 13 . 13 1Psi number (#) of wDi increments about our pi-Profiling Perimeters 1P 2.78416399841585 f3 being [ (pi)^2 ] / ( f2 ) / 4 ] quotient =~ 4.66926517525433 1Dc our companion value to 1PD . 1.03450713009732 wDi wDi =~ 1Ps / 4pi sum squared =~ 1.07020500222219 [wDi]^2 and our pi-Profiling Perimeters 1PD on 4, 1PD / 4 .
1.07020500222219 [wDi]^2 and our pi-Profiling Perimeters 1PD on 4, 1PD / 4 4 product =~ 4.28082000888877 1PD .
4.28082000888877 1PD inverse =~
0.233600104167795 being our Notional Electroweak Mixing Angle observed from wDi . .
4.28082000888877 1PD 4.66926517525433 1PDc our companion diameter value to 1PD quotient =~ 0.916808073265103 being our pi-Profiling Formula Facilitator 1Pe2 .
0.916808073265103 1Pe2 sum squared =~ 0.840537043204071 1Pe1
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0.840537043204071 1Pe1 5.09295817894065 f1 product =~ 4.28082000888877 1PD .
2.14041000444439 1PR radius 1PR 0.916808073265103 1Pe2 quotient =~ 2.33463258762717 1PRc our companion radius value to 1PR .
4.28082000888877 1PD 4 quotient =~ 1.07020500222219 1PDi being our pi-Profiling Perimeters diameter 1PD on 4, 1PD/4 .
1.07020500222219 1PDi being our pi-Profiling Perimeters diameter 1PD on 4, D/4 0.916808073265103 1Pe2 quotient =~ 1.16731629381358 1PDe our companion value to 1PDi .
4.28082000888877 1PD pi pi to 14 decimal places: pi14, rounding may be occurring product =~ 13.4485926912652 1P our pi-Profiling Perimeter 1P being [ wDi * 13 ] .
13.4485926912652 P our pi-Profiling Perimeter 1P being [ wDi * 13 ] 0.916808073265103 1Pe2 quotient =~ 14.6689291722417 1Pc our companion perimeter value to 1P .
14.6689291722417 1Pc our companion perimeter value to 1P 1.12837916709551 being the square root of 4/pi quotient =~ 13 1Psi number (#) of wDi increments about pi-Profiling Perimeter 1P .
5.09295817894065 f1 0.916808073265103 1Pe2 product=~ 4.66926517525433 1PDc our companion diameter value to 1PD .
1.03450713009732 wDi our pi-PF for wDi is: wDi =~ Ps / 4pi 0.957500952096187 1Pe3 quotient =~ 1.08042412681946 wDe our companion value to wDi
57.5710046841632 1PSsa, our pi-Profiling Perimeters companion Spheres surface area 4 quotient =~ 14.3927511710408 1PA our perimeters area 1PA
14.3927511710408 1PA our perimeters area 1PA 0.840537043204072 1Pe1 quotient =~ 17.1232800355551 Ac our companion area value to 1PA .
1.07020500222219 1PDi being our perimeters diameter 1PD on 4, 1PD/4 16 product =~ 17.1232800355551 1PAc our companion area value to area 1PA . . 14.3927511710408 1PA our perimeters area A 4 product =~ 57.5710046841632 1PSsa our pi-Profiling Perimeters companion Spheres surface area .