The universal real constant pi, the ratio of the circumference of any circle and its diameter, has no exact numerical representation in a finite number of digits in any number/radix system. It has conjured up tremendous interest in mathematicians and non-mathematicians alike, who spent countless hours over millennia to explore its beauty and varied applications in science and engineering. The article attempts to record the pi exploration over centuries including its successive computation to ever increasing number of digits and its remarkable usages, the list of which is not yet closed.

All circles have the same shape, and traditionally represent the infinite, immeasurable and even spiritual world. Some circles may be large and some small, but their ‘circleness’, their perfect roundness, is immediately evident. Mathematicians say that all circles are similar. Before dismissing this as an utterly trivial observation, we note by way of contrast that not all triangles have the same shape, nor all rectangles, nor all people. We can easily imagine tall narrow rectangles or tall narrow people, but a tall narrow circle is not a circle at all. Behind this unexciting observation, however, lies a profound fact of mathematics: that the ratio of circumference to diameter is the same for one circle as for another.

. 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. Emma Haruka Iwao grew up fascinated by pi. Now, she's computed over 31 trillion of its digits. Iwao set the newest Guinness World Record for the most accurate value of pi on Thursday.

Whether the circle is gigantic, with large circumference and large diameter, or minute, with tiny circumference and tiny diameter, the relative size of circumference to diameter will be exactly the same. In fact, the ratio of the circumference to the diameter of a circle produces, the most famous/studied/unlimited praised/intriguing/ubiquitous/external/mysterious mathematical number known to the human race. It is written as pi or as π –, symbolically, and defined as. Throughout the history of π, which according to Beckmann (1971) ‘is a quaint little mirror of the history of man’, and James Glaisher (1848-1928) ‘has engaged the attention of many mathematicians and calculators from the time of Archimedes to the present day, and has been computed from so many different formula, that a complete account of its calculation would almost amount to a history of mathematics’, one of the enduring challenges for mathematicians has been to understand the nature of the number π (rational/irrational/transcendental), and to find its exact/approximate value. The quest, in fact, started during the pre-historic era and continues to the present day of supercomputers. The constant search by many including the greatest mathematical thinkers that the world produced, continues for new formulas/bounds based on geometry/algebra/analysis, relationship among them, relationship with other numbers such as π = 5 cos − 1 ( ϕ / 2 ), π ≃ 4 / ϕ, where ϕ is the Golden section (ratio), and e i π + 1 = 0, which is due to Euler and contains 5 of the most important mathematical constants, and their merit in terms of computation of digits of π.

Right from the beginning until modern times, attempts were made to exactly fix the value of π, but always failed, although hundreds constructed circle squares and claimed the success. These amateur mathematicians have been called the sufferers of morbus cyclometricus, the circle-squaring disease. Stories of these contributors are amusing and at times almost unbelievable. Many came close, some went to tens, hundreds, thousands, millions, billions, and now up to ten trillion (10 13) decimal places, but there is no exact solution. The American philosopher and psychologist William James (1842-1910) wrote in 1909 ‘the thousandth decimal of Pi sleeps there though no one may ever try to compute it’. Thanks to the twentieth and twenty-first century, mathematicians and computer scientists, it sleeps no more. In 1889, Hermann Schubert (1848-1911), a Hamburg mathematics professor, said ‘there is no practical or scientific value in knowing more than the 17 decimal places used in the foregoing, already somewhat artificial, application’, and according to Arndt and Haenel (2000), just 39 decimal places would be enough to compute the circumference of a circle surrounding the known universe to within the radius of a hydrogen atom.

Further, an expansion of π to only 47 decimal places would be sufficiently precise to inscribe a circle around the visible universe that does not deviate from perfect circularity by more than the distance across a single proton. The question has been repeatedly asked why so many digits?

The verse 'gopi bhagya' basically follows Katapayadi system[0]. Earliest known usage of Katapayadi system was in 683 AD. That verse is from a 1965 book called 'Vedic Mathematics' by Bharati Krishna Tirtha Maharaja[1].

The Quora blog you linked has issues with terminologies and timelines of this specific 'Vedic Mathematics' book - such as calling these mental calculation techniques and tricks as Vedic even though there are no references to them in Vedas[2]. This is more of a political matter ;) And, it's already pointed out in the article linked by OP[3]. I'm quoting it here:

It must be pointed out that these sutras given by Tirtha Maharaja are created by the author himself, as stated in the introduction to his book, 'Vedic Mathematics' (published posthumously) and are therefore not actually Vedic.

These mathematical sutras are Vedic only in the sense that they are inspired by the Vedas in the mind of one dedicated to the Vedas. Thus the title 'Vedic Mathematics' is not correct.

[0]http://en.wikipedia.org/wiki/Katapayadi_system

[1]http://en.wikipedia.org/wiki/Vedic_Mathematics_%28book%29

[2]http://en.wikipedia.org/wiki/Bharati_Krishna_Tirthaji#Mathem..

Oh carolina riddim rarest money. [3]http://www.vedicsciences.net/articles/vedic-mathematics.html