Measuring the Immeasurable
Rhythm of 'Pi' Restored
Monday, March 07, 2011
Dear seekers of Truth,
This paper is only a glimpse of grace consequent to researching on the Grand Unification Theory of general relativity, quantum physics and superstrings (Paper due for submission shortly) in line with the songs of nuclear and particle physics sung at the height of enlightenment as "Thiru Arutpa" by the Saint Ramalinga Vallalar (1823-1874) who is still unknown to world as the supreme scientist. The convergence of singularity which spreads into a square and an irregular octagon encircling to infinity entwining the micro and macro, has been geometrically expressed in the architectural design of the Council of Truthful Wisdom constructed at Vadalur, Tamil Nadu, India. The council consecrated at the dawn of 1872 by the Saint infuses the very essence of spiritual unity in the fabric of humanity woven across the longitude and latitude of the planet earth. Therefore, it is considered more appropriate to disseminate the contents of this research paper to the seekers of truth congregating around the Council of Truthful Wisdom effectively represented by the non-commercial World Wide Web hosted in the name of Vallalarspace.com.
2. Squaring the Earth:
2.1. Euclid, (325 to 265 BC) the great geometric genius has laid down the base that the circumference of any circle divided by its diameter is to yield the quantum of Pi as the ratio between the diameter of the circle to its circumference remains always constant. Number is the most subtle expression of reality than any alphabet which by its complexity of construction approximates only to the proximity of truth. Therefore, while number unifies the world alphabet of any language however classic it may be, divides by its grammatical variations and cognate expressions. The sanctum of singularity inextricably linking the finite with the infinite breathes the fundamental cosmic essence in all eloquence within the shrines of civilizations constructed in exquisite architectural designs all over the earth. Pi precisely denoted by symbol 'π', the 16th lower case in the Greek alphabet is a symbolic expression of such essence with the infinite inscribed and the finite circumscribed within and without in an ethereal cosmic design.
2.2. Much water has since flown under the bridge of time immemorial even prior to the inscription of the value of Pi on a stone tablet by the Babylonians in 1900 BC. Still at the dawn of 2011, not only the masons of mathematics but also the most enlightened in its methods are yet to cognize that if at all the normalcy of Pi reels within the confines of irrationality and transcendence it is because of the method concocted by human intelligence. Consequently while one within by the variety of equations and infinite series of formulae is awed by the trillions and trillions of digits entailing, another without any equation is greatly intrigued by the enigma as to why finality of the finite in the quantum of Pi, still eludes the seekers of precision. Truth is always simple. Then, the means to such simplicity could not have involved any deployment of infinite series of complex formulae in its exploration. Therefore, it passes comprehension as to why the most methodical mathematicians for the past 4000 years have accomplished only the approximate and not the absolute value of Pi as it is evident from the Webs of Fame spread world wide.
3. Method in Madness:
3.1. Every mathematical society and every scientific magazine in this world declares it in the most unambiguous terms that no research paper which is being considered for publication elsewhere or any paper that is under consideration by any society or any magazine shall be submitted to them. In the event of their acceptance for publication, they deem it as a legal corollary to insist on the prospective authors to assign copyright categorically to such societies or to such magazines for sole dissemination of the contents of research world wide on their own. While to some extent the light of moon may be copyrighted to the planet earth which is our nest and the light of sun to all the planets with their satellites hovering around it, the shower of cosmic energy could never be interfered with as it spearheads on its own will through the rights of one part exercised against the whole in the universe.
3.2. Truth universal warrants absolute dissemination to the entire humanity transcending all barriers as every human being is unconditionally entitled to each and every morsel of such truth. If what is presented in this research paper is indisputable and unassailable, then, let it shall be sustained by itself on its own inherent strength. Therefore, in contra to such rights and regulations thereof, these precious seeds of precision sifted from the chaff of approximation are sown for germination as grains of harvest in the field of mathematics accessible to all alike for critical analysis and dissemination with a determination far and wide by all and for all.
4. Axis of Pi Tilted:
4.1. Whether it is a numeral or an alphabet, everything is constituted only by a series of dots. Therefore, singularity is a point. A straight line is between two points. The square is a straight line folded at four right angles (4x90°=360°). A circle is a straight line curved to meet its own ends at 360° without any angle in between. While the length of the square is its number of sides 4, the length of curve is approximately 3 of the 4 sides of the square. The side of the square and the diameter of the circle drawn within the square are always same. Whether the diameter of the circle is the side of the square or the hypotenuse of the square, the ratio between the diameter of the circle to its circumference drawn within a square or outside the square always remains constant. It is elementary arithmetic that if the side of the square is 1, then, the circumference of the square is exactly 4 measures of its side and the circumference of the circle is approximately 3 measures of its diameter or the side of the square. Therefore, as the circumference of the circle is not exactly 3 measures of its diameter but it is little more than that. The quantum in excess of 3 such measures together with the approximate 3 constitutes actually the quantum of Pi. It is history that despite search and re-search by the most innovative minds in mathematics, all such earnest activism to secure the accurate quantum in excess of the 3 measures of the diameter of the circle has consumed more than 4000 years till date.
4.2. The supercomputers in the world specifically configured by the most brilliant computing genii have spread the span of Pi as an unending arch of digits after the decimal, swelling into trillions and trillions on the road to infinity. It is recorded in the pages of web that the supercomputer designed at a cost of 1.5 million yen in Japan and deployed to scan the horizon of Pi from May to Aug 2010 has spotted only 5 trillion digits. The search for light not seen at the end of the tunnel of digits, is still going on somewhere on this globe to outnumber even the grains of sand spread along the beaches of this world only with intent to square the circle of Guinness and not to .
Let us have the glimpse of Pi just as a writing on a wall;
3.141592653 589793238 462643383 279502884 197169399 375105820 974944592 307816406 286208998 628034825 342117067 982148086 …………….to 5 trillion….
Still it goes on. Pi without a glimpse of any sequential repetition has been considered as the most irrational and transcendental as it cannot be the root of an algebraic equation as well.
4.3. Like the cosmic dust trailing behind any celestial comet, Pi's digital destination across the vault of mathematics as on date is not within the knowledge of any of the supercomputers or any of the human being who has designed such machines and developed their software. This world is yet to know that Pi, the supreme constant is not a mere mathematical expression but the very embodiment of universal unity entwining the finite with the infinite. It may be destiny that 4000 years of distorted mathematical history has to be set at right now at the dawn of 2011and Pi is to extricate itself from its confinement of approximation and consequently restore itself to its original grandeur of precision through a human instrument. It may be recalled that the great mathematician Ramanujan has also attributed the formulation of his much celebrated mathematical dictum in respect of Pi to the grace of divine revelation.
5. Eureka Enlightened:
5.1.While Euclid has laid down the basis that the circumference of any circle divided by its diameter yields the quantum of Pi, the statement of Archimedes in Proposition 3 of his treatise "Measurement of a Circle" specifies that the ratio of the circumference of any circle to its diameter is less than the fraction of 22/7 but greater than 223/71. Archimedes, the great mathematician and scientist had proceeded on the conviction that the circumference of the circle could only be approximated to proximity of accuracy by optimizing the sides of a polygon circumscribed around a circle.
5.2. Archimedes by increasing the number of polygons to 96 without the advantages of decimal system and zero has secured with mere pincers of fractions the quantum of Pi. Therefore, Pi approximated by Archimedes remains between the fractions of 22/7 and 223/71 equivalent in decimal system respectively to 3.142857142 to 3.14084507. In the realm of mathematics however precise may be the point of approximation, still its access to the matrix of truth remains a question because of the irrationality and transcendence of the result. The needle of accuracy between the scales of approximation continued to deflect between the two figures shown by Archimedes till such time it was settled at the present slot of 3.141592653 collectively by means of algorithm, calculus and trigonometry.
5.3. We may juxtapose the Pi of Archimedes and the Pi at present to appreciate the progress of approximation ultimately to truth with 9 as the side of the square and diameter of the circle.
As per Archimedes:
Value of Pi Area of circle Circum of circle
3.142857142 63.64285713 28.28571428
3.14084507 63.60211267 28.26760563
As per Pi at present:
Value of Pi Area of circle Circum of circle
3.141592653 63.61725122 28.27433388
It is pertinent to note that a polygon with any number of sides could never become a circle as the characteristics of the polygon and the circle are geometrically distinct even at infinity. No wonder even after the advent of the computer age, all the software developed and programmed in line with the method of Archimedes, the algorithm of Ramanujan and by other innovative methods devised by others to tame Pi by a host of computers lined up to work, either in succession or in unison exchanging the data collected whether online or offline, have failed in their mission because the search for accuracy was always displaced by the search for approximation of truth.
6. Beads of the Abacus:
6.1. The seed of Pi sprouts from the fraction of the circumference of the square and the circumference of the circle or the area of the square and the area of the circle. The ratio of the area of the square and the area of the circle or the circumference of the square and the circumference of the circle always remains constant at the fraction of 4/3. Therefore, if the side of the square is 4 (it can be any number), the ratio of the square and circle in the case of area as well as circle is calculated as follows:
Area of the square = 4
Area of the circle = 3
= 4÷3
= 1.333 333 333….to the infinite.
Circumference of the square = 4
Circumference of the circle = 3
= 4÷3
= 1.333 333 333….to the infinite.
6.2. Therefore, whatever may be the side of the square or the diameter of the circumference, the ratio between the square and the circle is always constant at 4/3 in fraction and 1.3333333333 in decimal. As the area of any square comprises of 9 units, the quantum is divided by 9, which is the composite and the third square number to obtain the ultimate if the side of the square is 1. It results in the excess 0.148148148 as it is evident from the calculation below;.
Therefore, = 1.3333333333……to the infinite
9
Excess = 0.148 148 148…………… to the infinite
If the above excess is added to the circumference of the circle 3 where the diameter of the circle is 1, the value of Pi works out to 3.148 148 148 …………………. repeating the sequence 3.148148148 148148148 148148148 148148148 148148148 148148148 148148148 148148148 148148148 148148148 148148148 148148148 148148148 148148148 148……….absolutely to infinity.
6.3. A pinch of salt, by no stretch of imagination could constitute the entirety of salt mined till date and contained in all the oceans but the taste of even a grain of salt has never distorted the experience of the absolute by any degree of approximation. In the same way, Therefore, Pi measures not only the entire span of infinity but also tastes all that infinite even within a grain of the finite. Pi is the universal constant unborn in mathematics and unrelated to any branch of science as it is the building block of the cosmic architecture.
6.4. Pi sprouts as the universal constant with its sequence of repetition which as it measures the instant of infinity and the extent of the finite alike. Therefore, it is the sequence of such repetition throughout infinity which is the ultimate proof that Pi is not only actively infinite but also potentially infinite. While it is the prerogative of Pi, it is not even the privilege of other constants in the universe in all the branches of sciences. Such sequence of repetition expressed in triplicate—3.148 148 148….. as displayed below constitutes the proof of accuracy. It is actively as well as potentially infinite as displayed hereunder;
The pyramid of pi
3
•
148
Infinity of the positive 148148
148148148
148148148148
148148148148148
148148148148148148
148148148148148148148
148148148148148148148148
148148148148148148148148148 Rushes to infinity
Returns to the finite 148148148148148148148148148
148148148148148148148148
148148148148148148148
148148148148148148
148148148148148
148148148148 Infinity of the negative
148148148
148148
148
•
3
6.4. Like the beads of quarks within the atom, like the code of genetics within the genes, the sequence of Pi bridges the finite with the infinite and anybody can recite the series of all the triplicate digits after the decimals up to infinity with all certainty. Consequently Pi becomes the very spirit of mathematics in its essence as it represents both the finite and infinity of the macro and micro at the stroke of the instant. It is said that infinity could not be measured or its quantum determined. But here one experiences as to what is infinity and the velocity of infinity. In comparison, even the fastest gallop of the super conductors in the most sophisticated computers in this world and why even the great speed of light at 3 lakh km per second pales into insignificance just as a limping horse galloping within a snail's pace. Albert Einstein would have been rendered speechless at the velocity of Pi which is the velocity of infinity where there is no trace of time and space.
7. Taste of the Tables:
7.1. In order to appreciate the difference between the amount of accuracy inherent in the re-determined Pi and the Pi at present, a table is drawn. It could be seen from the table that at the diameter of 9, the area of the circle is 63.75 and at 18, the area is 255. Just as the span of 27 stars of the zodiac fulfills the 360°, so also the wave of Pi at every 27th sequence repeats the quantum of circumference and area of the circle to full number as it is evident from the table below; at the diameter of 27, the circumference of the circle is 85 and the area is 573.75. At the diameter of 54, the circumference is 170 and the area is 2295 and so on. It could also be seen from the table below that while the value of Pi 3.148148148 returns to full number in the case of both circumference and area, the value of Pi at present—3.141592653 is caught up in a net of fractal web. In all such measures, one can see the values of circumference and area in respect of Pi at present struggle to stabilize with any certainty.
| Diameter Circumference Area Circumference Area Side Pi 3.148148148 Pi 3.141592653 |
| 1 3.148148148 0.787037037 3.141592653 0.785398163 |
| 2 6.296296296 3.148148148 6.283185306 3.141592653 |
| 3 9.444444444 7.083333333 9.424777959 7.068583469 4 12.59259259 12.59259259 5 15.74074074 19.67592593 6 18.88888888 28.33333333 7 22.03703704 38.5648148 8 25.18518518 50.37037037 |
| 9 28.333333333 63.75 28.27433388 63.61725122 |
| 12 37.777777777 113.333333333 37.69911184 113.0973355 |
| 18 56.666666666 255 56.54866775 254.4690049 |
| 24 75.555555555 453.333333333 75.39822367 452.389342 |
| 27 85 573.75 84.82300163 572.555 |
| 54 170 2295 169.6460033 2290.221 |
| 108 340 9180 339.2920065 9160.884 |
| 216 680 36720 678.584013 36643.5367 |
| 432 1360 146880 1357.168026 146574.146 |
| 864 2720 587520 2714.336052 586296.587 |
| 1728 5440 2350080 5428.672104 2345186.349 |
8. Oracle of the Octagon
8.1. Every geometrical shape drawn within the square has got a definite relationship with the square. With the side of the square as 9 a table is drawn below with the columns reflected therein. In the case of circle both the figures of Pi at present and modified are shown. It is quite natural that as the figures have been drawn within the square, the dimensions of other geometrical figures are lesser than that of the square. In the case of regular octagon the area is 63 and the circumference is 28. But in the case of the irregular octagon the area is still 63 but the circumference is 28.9705. It is because in the regular octagon, all the 8 sides are equal but in the case of irregular, out of the 8 sides 4 are from the hypotenuse in line with Pythagorean Theorem. However the sum total of area and circumference of octagon whether regular or irregular ought to be less than that of the circle.
_______________________________________________________________
Geo Shape Area Circumfer % Total
_______________________________________________________________
Square 81 36 2.25 117
Reg. Oct 63 28 2.25 91
Irreg. Oct 63 28.9705 2.17 91.9705627
Circle:
Ongoing Pi 63.61725122 28.27433388 2.25 91.8915851
Pi modified 63.75 28.333333333 2.25 92.0833333
Archimedes 63.64285713 28.28571428 2.25 91.92857141
________________________________________________________________
8.2. The sum total of the area and the circumference of the circle could never be lower than that of the irregular octagon. It is impermissible within the logical dictum of mathematics. It is evident from the above that though the sum total of circle (91.89) with the ongoing Pi (3.141592653) is more than that of the regular octagon (91), it is less than the sum total of the irregular octagon (91.97). But the sum total of the circle (92.08) with the modified Pi (3.148148148) is more than the sum total of the irregular octagon (91.97). Even the maximum of Archimedes which works out to a total of 91.92857141 falls short of the sum total (91.97) of the irregular octagon. It is not only an unassailable yardstick to uphold accuracy of the modified Pi 3.148148148 but also exposes the incurable infirmity inherent in the ongoing Pi 3.141592653. Even if the accuracy is questioned, still its proximity to truth more than the reigning Pi 3.141592653 could never be mathematically disputed. Therefore, it is the only independent yardstick of comparison whose veracity could never be faulted by any stretch of infinite series of formulae.
9. Correction in a Fraction:
9.1. Archimedes had held that the value of Pi has got to be in between the fractions of 22/7 and 223/71. At that time of Archimedes decimal system was not in practice. The fractions are equivalent to the decimals 3.142857142 and 3.14084507. Therefore, if the area of the circle is calculated with 9 as the side of the square (diameter of the circle) then the entire calculation could be presented in the following table;
______________________________________________________________
Value of Pi Circle
Fraction Decimal Area Circumference
22/7 3.142857142 63.64285713 28.28571428
223/71 3.14084507 63.60211267 28.26760563
_________________________________________________________________
It may be recalled that the value of Pi emanates from the fraction of 81/73 where 81 is the area of the square with side 9 and 63 is the area of the octagon. It also springs from the fraction 36/28 where 36 is the circumference of the square and 28 is the circumference of the regular octagon. Therefore, if we equate the Pi born out of the ratio between square and a regular octagon to the Pi emerging out of the ratio between the square and the circle, then an irreparable damage sets in and everything goes awry.
9.2. Archimedes had proposed to bring the area of the circle to the maximum of 63.64285713 with the fraction of Pi 22/7 equivalent to the decimal 3.142857142. But in effect Pi has to move further up from 3.142857142 to 3.160493827 as shown below. If 63 is to be treated as the area of the circle then Pi is 3.111111111. If 64 is to be treated as the area of the square, then Pi is 3.160493827.
Area Value of Pi Area of circle
_________________________________________
63 3.111111111 63
64 3.160493827 64
__________________________________________
Here the value of Pi returns the basic area of the circle again but it is not so in the above case where it is more than the value of the area adopted for calculation.
9.3. While what Archimedes had proposed is a descent in the case of 3.142857142 to 3.14084507, it ought to have been an ascent in the case of 3.11111111 to 3.160493827. Therefore, the value of Pi has got to move up from 3.11111111 to 3.160493827 and not to go down from 3.142857142 to 3.14084507. In other words, the value of Pi ought to have been fixed between 3.142857142 and 3.160493827. We may see that the value of modified Pi 3.148148148 (area 63.75 and circumference 28.333333333) falls into the slot between 3.142857142 and 3.160493827. But in the case of the ongoing Pi 3.141592653, it falls far short of the boundary. The maximum of Archimedes which works out to a total of 91.92857141 (area + circumference) as shown in para 8.1. above, falls short of the sum total of the irregular octagon 91.9705627 (area + Circumference). Actually the sum total of the area and circumference of the circle is below that of the square and that of the irregular octagon. Therefore, when it is not only logically inappropriate but also mathematically inaccurate, is it proper to measure the equatorial circumference of our earth by the gauge of the ongoing Pi?
10. Tentacles of the Octopus
10.1. It is not only in the case of square and circle but also in the case of square and the octagon whether regular or irregular, the ratio remains constant as any geometrical shape drawn within a square has got a mathematical relationship with the square. Therefore, in the case of the ratio between the square and the octagon whether regular or irregular also we can experience the repetition of digits-- 3.142857 142857 142857 142857 142857 142857 142857 142857…. to infinity. Therefore, just as the ratio between the octagon and square results in a repetition of sequence, so also the proof of accuracy of Pi is rendered by the repetition of sequence inherent in the ratio between the square and the circle.
10.2. If the side of the square is 9, then the area of the square is 81. While the square is 9 units the octagon is 7 units and therefore, the area of the octagon is 63 (9x7). While the circumference of the square is 4 units 36 (9x4), the circumference of the octagon is also 4 units 28 (7x4). Therefore, the ratio of area of the square and the area of the octagon is always constant and it is not required to be added as the area and the circumference of the octagon which unlike that of the circle are accurate to the core.
Area of the square/ area of the octagon = 81/63 = 9/7
Circum of square/circum of the octagon = 36/28 = 9/7
In both the cases, 9/7 = 1.285714286
Ratio = 1.285714286
9
= 0.142857142……….to infinity.
10.3. In the same way, if we equate the fraction 4/3 to the sum total of area (9x9=81) and the circumference (9x4=36) of the square divided by the sum total of the area (8x8=64) and circumference (3x9=27) of the circle, we get the same ratio as shown below;
Sum total of square = 81+36 = 117 (area+circum)
Sum total of circle = 64 +27 =91 (area+circum without Pi correction)
In both the cases = 117/97 = 13/9
Ratio = 1.285714286
= 1.285714286
9
= 0.142857142…..to infinity
It is this quantum which repeatedly occurs in various combinations as explained above has been added to 3 and made as Pi = 3.142857142 equivalent to the fraction of 22/7. Therefore, it is evident that the fraction of 22/7 equivalent to 3.142857142 pertains to the ratio of the square and the octagon. In the same way the fraction of 22/7 equivalent to 3.142857142 also occurs in the ratio of the square and circle without addition of the element of Pi. Therefore, just as the ratio between the octagon and square results in a repetition of sequence, so also the repetition of sequence inherent in the ratio between the square and the circle is the proof of accuracy of Pi. Such a constant repetition of the sequence --0.142857 142857 142857 142857 142857 142857 142857 142857….. to infinity runs parallel to the still more constant repetition of 0.148148148 148148148 148148148 148148148 148148148 148148148 ……….absolutely to infinity..
11. Decorating the Mummies:
11.1. A numerator is a number above the line in a fraction and a denominator is a number below the line in a fraction showing how many parts the whole is divided into. In the fraction of 4/3, square plays the role of a whole as numerator and circle as the denominator played its role as a part. But in the fraction of ¾, circle as 3 denoted denominator the infinite and 4 as a square plays the part is denoting the finite.
Before Pi the ratio is = ¾ = 0.75
After Pi the ratio is = 3.148148148
4
= 0.787037037
If 0.75 is deducted then it is 0.787037037—0.75 = 0.037037037…..to infinity
11.2. Whether the square is a numerator or the circle is the numerator or in words whether square is treated as the infinite or the whole or the circle is treated as the infinite, the sequence repeats to infinity which is the proof that the modified Pi is devoid of any infirmity.
But in the case of the Pi at present,
the ratio is = 3.141592653
4
= 0.785398163
If 0.75 is deducted then it is 0.785398163—0.75 = 0.035398163……….to infinity.
There is no repetition and therefore there is no consequence of any sequence.
12. Orphaned Accuracy
12.1. Only in respect of the square drawn within the circle, there arises the necessity to increase the number of polygons to find the arc on the side of the hypotenuse by adopting one quarter of the square within the circle as a right angled triangle with two equal sides. The process is to spread the hypotenuse of the square to coincide with the arc of the circle. If the method adopted is to approximate area of the square with the circumference of the circle drawn outside the square, then such a flight could never land in accuracy. But in respect of the circle drawn within the square, such a complication does not arise as it is a simple correlation between the square and circle.
12.2. Archimedes ought to have correlated either the area of square @ side 9 (9x9) with the area of the circle (4.5 x 4.5 x Pi) or correlated the circumference of the square (9 x 4) with the circumference of the circle (9 x 3) to work out the ratio between the diameter of the circle to its circumference. Just as the circumference of the circle at the diameter of 9 with Pi as 3 works out to 27, so also the area of the circle works out to 60.75. Therefore, instead of adopting 81/63 which is the ratio of the area of square and an octagon either regular or irregular, the ratio 81/60.75 of the area of square and circle ought to have been considered. Alternatively, Archimedes could have adopted either the circumference of the square (9 x 4 =36) or circumference of the circle (9 x 3 =27) to work out the ratio. In both the cases, the ratio between the circumferences and the areas remains one and the same as 1.333333333…..to infinite.
12.3. Therefore, the adoption of the wrong saddle led Archimedes to rein the horse of Pi with the ratio of 1.285714286 which restricted its gallop never beyond 3.142857142. As increasing the quantum of Pi would tantamount to increasing the quantum of ratio beyond 1.285714286 thereby beyond the excess of 0.142857142, everyone subsequent to Archimedes orphaned accuracy and adopted the approximate as the quantum of Pi. Having stabilized Pi at the orbit of 3.141592653, they have since been enchanted by stretching the incorrect tail of Pi towards infinity.
13. Algorithm of Ramanujan
13.1. With due respects to the great mathematical genius, it is stated in all sincerity that the same mathematical infirmity found in the case of Archimedes and all the mathematicians and amateurs alike is also inherent in the series of formulae devised to approximate Pi by the great mathematician Ramanujan. He had also circumscribed his formula to approximate Pi with the limitation of 22/7 equivalent to the decimal 3.142857142. Consequently, there was no opportunity for the quantum of Pi to extricate itself from the confines of calculated approximation to see the light of accuracy any longer for yet another millennium till date. It cannot be said that as the decimal system was not then in operation, the approximation lingered on. Even today with the advent of super conductors operating the computing drives to trillions of times faster within a fraction of a second, none has chosen to question the perfection of Pi but remains fascinated only by the extension of its digital tail to infinity.
14. Galloping on the Snail:
14.1 The value of Pi as it is available today is the outcome of the combination of a mathematical master and a computing genie. One is the human mind and another is the machine which however precise is not the master of the mind which programmed it. Therefore, without examining the veracity of the statement of Archimedes, the mind and the machine followed the needle of approximation deflecting between two fractions 22/7 and 223/71 vying with each other to perfect the statue of Pi chiseled by increasing the number of polygons to infinity.
14.2. It is a mathematical history that in Aug 2009, Japanese Supercomputer T2K Open Supercomputer calculated Pi to 2,576,980,377,524 digits in 73 hrs and 36 mts. In December 2009, it took a total of 131 days to compute 2,699,999,990,000 decimal digits for calculation, conversion and verification. In Aug 2010, it took a total of the period from May 4 to August 3 to compute 5,000,000,000,000 decimal digits on a home computer designed for the purpose and consuming 64 and 66 hrs for primary and secondary verification. All these exercises have been rendered null and void by this research which has determined the orbit of Pi accurately at 3.148148148 to infinity. Now, it could be demonstrated that by a mere touch of a scientific calculator, Pi touches infinity and all the digits flowing up to infinity return to the decimal singularity instantly without the poles of time and space.
15. Reflection of the Refraction:
15.1. Pi is the supreme constant among the constants in this world. Therefore, it is the universal constant. Therefore, this modified quantum of Pi is not transcendental and irrational. A thoughtful review of the mathematical history lays bare the fact that we have only attributed to Pi a quantum which we consider as correct and since then, Pi has been adjudged all along as the most irrational number with all our randomness reflected on it as a writing on a wall, as shown herein—Pi =
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086 …………….to more than 5 trillion digits as on date;
15.2. Now it has been proved beyond doubt that the accuracy of Pi could never be disputed in the realm of mathematics and therefore, Pi is no longer a mere approximation of truth; it is an embodiment of accuracy and its rationality is unquestionable. It makes us experience in all reality what is infinity without time and space by the very sequence of its repetition gushing from the finite to the infinite and from the infinite to the finite as demonstrated herein---
Pi =
3.148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148……………………..to infinity and back to the finite.
16. Testament and Temple:
16.1 The passages of the Old Testament of any version, 1 Kings 7:23 and 2 Chronicles 4:2 are synonymous in their mathematical as well as in their spiritual import. A conjoint reading of the two chapters in the light of the verses mentioned above disclose the measurement devised by King Solomon for the temple he had built for God in Jerusalem. The king had designed the temple in the measurement of 20 cubit x 20 cubit. Within that temple he built an altar with a circle of 30 cubit circumference having a diameter of 10 cubit as radius and 5 cubit serving as its height. The structure was cast within a square having a side of 10 cubit and a circumference of 40 cubit (10 x 4 = 40).
16.2. The square with a side 10 cubit which served as the diameter of the circle inlaid together with the 12 oxen facing all the four directions of three each vouch for ample evidence to uphold the universal fraction of 4/3 which has given birth to Pi. The ratio between the circumference of the square and the circumference of the circle results in the same 1.333333333…….which when divided by 9 to arrive at the quantum in excess of 3, yields 0.148 148 148….to infinity. When put together they constitute the universal constant Pi 3.148148148….to infinity. But the church and the retinue of researchers have missed the lesson Pi in the altar of the temple built by King Solomon to God.(Dealt with in a separate paper-Fundamental Unity).
17. Constant on the Coast:
17.1. The decimal is the circle micro in infinity and the space of infinity is the opposite of the macro. The dot spreads into a square and a square into an octagon. It is curled into a circle to a square again and reduced to a dot. The process is endless. The dot is the building block of both the number and the alphabet. The micro of the micro and the macro of the macro are infinite but the micro of the macro and macro of the micro are finite in nature. The finite and the infinite form the warp and weft of this universe. Pi is a universal constant connecting both infinite and finite. The concept of Pi discloses that infinite in the negative becomes the finite in the positive and the finite in the negative becomes infinite in the positive.
17.2. The decimal in Pi represents the singularity of the finite and the infinite and 1 the side of square or diameter of the circle, 4 represents the full square and 8 represents the irregular octagon and the unseen circle swirling within the square. The circle is the force which spirals the singularity to infinity and retrieves the infinity to singularity through a square and an irregular octagon. Now the sequence is repeated as the square returns to the circle and circle to octagon and octagon to square and the square reduced to its side and becoming a decimal in the form of a dot like the tides of ocean incessantly breaking on the shores and withdrawing. A pinch of salt, by no stretch of imagination could constitute the entirety of salt mined till date and contained in all the oceans but the taste of even a grain of salt has never distorted the experience of the absolute by any degree of approximation. In the same way, Therefore, Pi measures not only the entire span of infinity but also tastes all that infinite even within a grain of the finite.
18. Genesis of Genetics:
18.1. Pi is not the quantum isolated in mathematics alone but connected with all in the universe not as a mere mathematical constant but as an all pervasive universal constant. It is proved by the code of genetics too. The genetic code comprises of 64 triplets of nucleotides. These triplets are called codons. The genetic code could be expressed as either RNA codons UCAG or DNA codons TCAG. But it occurs in triplicate of any of the four. It may be UAG in the case of RNA or TAC in the case of DNA or any other combination in triplicate as appropriate in the genetic application. The 4/3 combination of the code in reserve and the code in utilization bears a strange coincidence to the ratio in the fraction of square and circle. Every RNA or DNA codons have 4 expressions making the 16 slots into (16x4) 64 in all which incidentally corresponds closer to the area of the circle. (Being dealt with in a separate research paper under Genesis of Genetics)
19. Unborn and Unrelated:
19.1. Pi is neither a mathematical number nor a scientific number. Pi is unborn and therefore it is only unrelated to any science and but also to any civilization its origin is unknown. All these years, it is we who have invested the element of irrationality into the pristine purity of Pi which spreads like the tress of a peacock across the vault of immensity of the immeasurable in its numerical excellence of 3•148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148…..Therefore, the day when the whole world congregating in a conscientious congress would rise in unison to accept the exact quantum of Pi unalloyed by any approximation, is not far behind but is round the corner. This paper has not employed any method of algebra, calculus, geometry, trigonometry or any infinite series of complex formulae but truth has been simply borne out only by the elegance of elementary arithmetic. In all humbleness, I may resonate the saying of Shakespeare from the words of Polonius in 'Hamlet':
"Though this be madness, yet there is method in it".
19.2. Without disturbing the tranquility in the sepulchral silence, we may by consensus seek to obliterate the value of Pi engraved in the tombstone of Ludolph van Celeun in Leiden, the Netherlands in 35 digit approximation and re-engrave the new value of Pi to honour the beautiful sense of pride, the Dutch mathematician was cherishing when he used 60 doublings of an inscribed square to obtain the first 35 digits of Pi. It is needless to mention that Pi was the monarch of all it surveyed for centuries in the realm of mathematics as Ludolph Constant. Let the intrinsic worth of this paper may be judged by both the specialists and the ordinary alike and truth be declared and upheld.
If it is truth, then, let such truth shall be sustained by itself on its own inherent merits.
20. For Whom the Bell Tolls?
20.1. With all humility in my heart, I recall the battle scene in the "Bhagavat Gita". Opposite to my side are the nameless Great Masters of Babylonia, Egypt and Greek, Archimedes, Ptolemy, Aryabhatta, Isaac Newton, Chinese and Persian Masters, Ramanujan and the invincible Robots in the guise of Supercomputers. But unmindful of their status of celebrity, minding only the state of falsity in the field of Pi, with my fingers of frailty I arched the mighty bow of truth with no arrow left in the quilt. Even when the resonance of the string of bow still rattled, just as the neutrinos pass through the matter unhindered, the arrow of accuracy not only pierced infinity but also returned to the quilt of finite instantly
In all Reverence and Gratitude,
Before the Unknown and the Known,
Dedicating and bequeathing to the Humanity for posterity,
Written on behalf of the seeker in everyone,
With all the regards,
Sivajayakumar.
E mail: ssivajayakumar@gmail.com
Coimbatore, India.
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