Amazing Wisdom!!!!

. Finds errors with Shanks value of Pi starting with the 528th decimal place. Gives correct value to the 710th place – J.W. Works with Ferguson to find 808th place for Pi Used Machin’s formula + + = 1985 1 arctan 20 1 arctan 4 1 3arctan 4 p.

The sanskrit verse for the value of ‘pi’

http://www.gosai.com/chaitanya/saranagati/html/vedic-age_fs.html under ‘vedic mathematics’

“In order to help the pupil to memorize the material studied and assimilated, they made it a general rule of practice to write even the most technical and abstruse textbooks in sutras or in verse (which is so much easier-even for the children-to memorize). And this is why we find not only theological, philosophical, medical, astronomical, and other such treatises, but even huge dictionaries in Sanskrit verse!

So from this standpoint, they used verse, sutras and codes for lightening the burden and facilitating the work (by versifying scientific and even mathematical material in a readily assimilable form)!” [8]

The code used is as follows:

The Sanskrit consonants

ka, ta, pa, and ya all denote 1;
kha, tha, pha, and ra all represent 2;
ga, da, ba, and la all stand for 3;
Gha, dha, bha, and va all represent 4;
gna, na, ma, and sa all represent 5;
ca, ta, and sa all stand for 6;
cha, tha, and sa all denote 7;
ja, da, and ha all represent 8;
jha and dha stand for 9; and
ka means zero.

Vowels make no difference and it is left to the author to select a particular consonant or vowel at each step.

This great latitude allows one to bring about additional meanings of his own choice. For example kapa, tapa, papa, and yapa all mean 11. By a particular choice of consonants and vowels one can compose a poetic hymn with double or triple meanings.

Here is an actual sutra of spiritual content, as well as secular mathematical significance.

gopi bhagya madhuvrata
srngiso dadhi sandhiga
khala jivita khatava
gala hala rasandara

While this verse is a type of petition to Krishna, when learning it one can also learn the value of pi/10 (i.e. the ratio of the circumference of a circle to its diameter divided by 10) to 32 decimal places. It has a self-contained master-key for extending the evaluation to any number of decimal places.

The translation is as follows:

O Lord anointed with the yogurt of the milkmaids’ worship (Krishna), O savior of the fallen, O master of Shiva, please protect me.

At the same time, by application of the consonant code given above, this verse directly yields the decimal equivalent of pi divided by 10: pi/10 = 0.31415926535897932384626433832792. Thus, while offering mantric praise to Godhead in devotion, by this method one can also add to memory significant secular truths.

(explanation: go/ga =3, pi/pa =1, bhag =4, ya =1, ma =5, dha =9, ra =2, ta =6 and so on.)

.The number π ( ) is a. Originally defined as the of a 's to its, it now has various equivalent definitions and appears in many formulas in all areas of. It is approximately equal to 3.14159. It has been represented by the Greek letter ' since the mid-18th century, though it is also sometimes spelled out as ' pi'. It is also called Archimedes' constant.Being an, π cannot be expressed as a (equivalently, its never ends and never ). Still, fractions such as 22/7 and other rational numbers are commonly used to π. The digits appear to be.In particular, the digit sequence of π is conjectured to satisfy a, but to date, no proof of this has been discovered.

Also, π is a; that is, it is not the of any having.This transcendence of π implies that it is impossible to solve the ancient challenge of with a.required fairly accurate computed values to approximate π for practical reasons, including the. Around 250 BC the created an algorithm for calculating it. In the 5th century AD approximated π to seven digits, while made a five-digit approximation, both using geometrical techniques. The historically first exact formula for π, based on, was not available until a millennium later, when in the 14th century the was discovered in Indian mathematics. In the 20th and 21st centuries, mathematicians and discovered new approaches that, when combined with increasing computational power, extended the decimal representation of π to many trillions of digits after the decimal point. Practically all scientific applications require no more than a few hundred digits of π, and many substantially fewer, so the primary motivation for these computations is the quest to find more efficient algorithms for calculating lengthy numeric series, as well as the desire to break records. The extensive calculations involved have also been used to test and high-precision multiplication.Because its most elementary definition relates to the circle, π is found in many formulae in and, especially those concerning circles, ellipses, and spheres.In more modern, the number is instead defined using the spectral properties of the system, as an or a, without any reference to geometry.

It appears therefore in areas of mathematics and the sciences having little to do with the geometry of circles, such as and, as well as in almost all areas of. The ubiquity of π makes it one of the most widely known mathematical constants both inside and outside the scientific community. Several books devoted to π have been published, and record-setting calculations of the digits of π often result in news headlines. Attempts to with increasing precision have led to records of over 70,000 digits. Contents.Fundamentals NameThe symbol used by mathematicians to represent the ratio of a circle's circumference to its diameter is the lowercase, sometimes spelled out as pi, and derived from the first letter of the Greek word perimetros, meaning circumference.In English, π is ( ). In mathematical use, the lowercase letter π (or π in font) is distinguished from its capitalized and enlarged counterpart ∏, which denotes a, analogous to how ∑ denotes.The choice of the symbol π is discussed in the section.Definition.

Because π is a, is not possible in a finite number of steps using the classical tools of.In addition to being irrational, more strongly π is a, which means that it is not the of any non-constant with coefficients, such as x 5 / 120 − x 3 / 6 + x = 0.The transcendence of π has two important consequences: First, π cannot be expressed using any finite combination of rational numbers and square roots or such as 3√ 31 or √ 10. Second, since no transcendental number can be with, it is not possible to '. In other words, it is impossible to construct, using compass and straightedge alone, a square whose area is exactly equal to the area of a given circle. Squaring a circle was one of the important geometry problems of the.

Amateur mathematicians in modern times have sometimes attempted to square the circle and sometimes claim success despite the fact that it is mathematically impossible.Continued fractions. See also: AntiquityThe best-known approximations to π dating were accurate to two decimal places; this was improved upon in in particular by the mid-first millennium, to an accuracy of seven decimal places.After this, no further progress was made until the late medieval period.Based on the measurements of the (c. 2560 BC), some Egyptologists have claimed that the used an approximation of π as 22 / 7 from as early as the.This claim has met with skepticism.The earliest written approximations of π are found in and Egypt, both within one percent of the true value. In Babylon, a dated 1900–1600 BC has a geometrical statement that, by implication, treats π as 25 / 8 = 3.125. In Egypt, the, dated around 1650 BC but copied from a document dated to 1850 BC, has a formula for the area of a circle that treats π as ( 16 / 9) 2 ≈ 3.16.Astronomical calculations in the (ca. 4th century BC) use a fractional approximation of 339 / 108 ≈ 3.139 (an accuracy of 9×10 −4).Other Indian sources by about 150 BC treat π as √ 10 ≈ 3.1622.

Polygon approximation era.Π can be estimated by computing the perimeters of circumscribed and inscribed polygons.The first recorded algorithm for rigorously calculating the value of π was a geometrical approach using polygons, devised around 250 BC by the Greek mathematician. This polygonal algorithm dominated for over 1,000 years, and as a result π is sometimes referred to as 'Archimedes' constant'.Archimedes computed upper and lower bounds of π by drawing a regular hexagon inside and outside a circle, and successively doubling the number of sides until he reached a 96-sided regular polygon. By calculating the perimeters of these polygons, he proved that 223 / 71. Developed the polygonal approach to approximating π.In, values for π included 3.1547 (around 1 AD), √ 10 (100 AD, approximately 3.1623), and 142 / 45 (3rd century, approximately 3.1556).Around 265 AD, the mathematician created a and used it with a 3,072-sided polygon to obtain a value of π of 3.1416.

Liu later invented a faster method of calculating π and obtained a value of 3.14 with a 96-sided polygon, by taking advantage of the fact that the differences in area of successive polygons form a geometric series with a factor of 4. The Chinese mathematician, around 480 AD, calculated that 3.1415926.

Comparison of the convergence of several historical infinite series for π. S n is the approximation after taking n terms. Each subsequent subplot magnifies the shaded area horizontally by 10 times.The calculation of π was revolutionized by the development of techniques in the 16th and 17th centuries.An infinite series is the sum of the terms of an infinite. Infinite series allowed mathematicians to compute π with much greater precision than and others who used geometrical techniques.

Although infinite series were exploited for π most notably by European mathematicians such as and, the approach was first discovered in sometime between 1400 and 1500 AD. The first written description of an infinite series that could be used to compute π was laid out in Sanskrit verse by Indian astronomer in his, around 1500 AD. The series are presented without proof, but proofs are presented in a later Indian work, from around 1530 AD.Nilakantha attributes the series to an earlier Indian mathematician, who lived c. 1350 – c. 1425. Several infinite series are described, including series for sine, tangent, and cosine, which are now referred to as the. Madhava used infinite series to estimate π to 11 digits around 1400, but that value was improved on around 1430 by the Persian mathematician, using a polygonal algorithm.

It’s hard work to reverse engineering and time-consuming. Warband script enhancer steam.

Main article:is the practice of memorizing large numbers of digits of π, and world-records are kept by the. The record for memorizing digits of π, certified by Guinness World Records, is 70,000 digits, recited in India by Rajveer Meena in 9 hours and 27 minutes on 21 March 2015.

In 2006, a retired Japanese engineer, claimed to have recited 100,000 decimal places, but the claim was not verified by Guinness World Records.One common technique is to memorize a story or poem in which the word lengths represent the digits of π: The first word has three letters, the second word has one, the third has four, the fourth has one, the fifth has five, and so on. An early example of a memorization aid, originally devised by English scientist, is 'How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.' When a poem is used, it is sometimes referred to as a piem. Poems for memorizing π have been composed in several languages in addition to English.Record-setting π memorizers typically do not rely on poems, but instead use methods such as remembering number patterns and the.A few authors have used the digits of π to establish a new form of, where the word lengths are required to represent the digits of π.

The contains the first 3835 digits of π in this manner, and the full-length book Not a Wake contains 10,000 words, each representing one digit of π. In popular culture.

The circular shape of makes it a frequent subject of pi.Perhaps because of the simplicity of its definition and its ubiquitous presence in formulae, π has been represented in popular culture more than other mathematical constructs.In the 2008 and documentary co-production, aired in October 2008 on, British mathematician shows a of the – historically first exact – when visiting India and exploring its contributions to trigonometry.In the (a science museum in Paris) there is a circular room known as the pi room. On its wall are inscribed 707 digits of π. The digits are large wooden characters attached to the dome-like ceiling.The digits were based on an 1853 calculation by English mathematician, which included an error beginning at the 528th digit. The error was detected in 1946 and corrected in 1949.In 's novel it is suggested that the creator of the universe buried a message deep within the digits of π.

The digits of π have also been incorporated into the lyrics of the song 'Pi' from the album by.In the United States, falls on 14 March (written 3/14 in the US style), and is popular among students. Π and its digital representation are often used by self-described 'math ' for among mathematically and technologically minded groups. Several college at the include '3.14159'.

Pi Day in 2015 was particularly significant because the date and time 3/14/15 9:26:53 reflected many more digits of pi. In parts of the world where dates are commonly noted in day/month/year format, July 22 represents 'Pi Approximation Day,' as 22/7=3.142857.During the 2011 auction for 's portfolio of valuable technology patents, made a series of unusually specific bids based on mathematical and scientific constants, including π.In 1958 replacing π by τ, where τ = π/2, to simplify formulas.However, no other authors are known to use τ in this way. Some people use a different value, τ = 2 π = 6.28318., arguing that τ, as the number of radians in one, or as the ratio of a circle's circumference to its radius rather than its diameter, is more natural than π and simplifies many formulas.

Celebrations of this number, because it approximately equals 6.28, by making 28 June 'Tau Day' and eating 'twice the pie', have been reported in the media. Solaris performance tools pdf download. However, this use of τ has not made its way into mainstream mathematics.In 1897, an amateur mathematician attempted to persuade the to pass the, which described a method to and contained text that implied various incorrect values for π, including 3.2.The bill is notorious as an attempt to establish a value of scientific constant by legislative fiat.

The bill was passed by the Indiana House of Representatives, but rejected by the Senate, meaning it did not become a law. In computer cultureIn contemporary, individuals and organizations frequently pay homage to the number π. For instance, the let the version numbers of his program approach π. Value Of Pi In FractionThe versions are 3, 3.1, 3.14, and so forth.rseverything.