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2015-05-18T18:27:09+05:30

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Pi   = π = 22/7 (nearly) =  3.14159 approximately.
Pi  is a mathematical constant.  It is precisely  defined as the ratio of a circle’s circumference (perimeter) to its diameter.  The Greek letter  π  is given by an English mathematician William Jones in early 18 th century AD.  But only after famous Leonhard Euler started using it in his works Mechanica, during 1940s, others have accepted the Greek letter.

Pi  is an irrational number.   22/7 or 3.14 is only approximate value, for our computational  ease.  Pi is a transcendental number.

Chinese and Indians calculated pi to 5 digits by the 5th century CE.   BrahmaGupt  also calculated pi using geometrical means.   In the 14th century, Madhava  discovered a series called Madhava-Leibniz series to find pi.
Now, after the advent of computers, various educational institutes and enthusiasts have computed pi to large number of digits.  Recently in 2014 , pi has been computed to 13 trillion digits  and it had taken a few months do that.   They do this for breaking world records.

Pi is mainly useful in geometry and all the areas of science and mathematics where geometry is used.   So it forms part of  even cosmology, number  theory, trigonometry ,  probability distributions, complex numbers,  statistics, thermodynamics, mechanics, electromagnetism (Coulombs’ law).  The  computations of areas and volumes of circular, elliptical, spherical, cylindrical objects are all based on Pi.

    The well known  simple pendulum ‘s time period is calculated using  Pi, length of the pendulum and gravity.

    In Quantum mechanics,  there is an important principle called Heisenberg’s uncertainty principle.  It states that momentum and position of a  particle can be specified only with a maximum precision of Planck’s constant divided by 4 Pi.
General theory of relativity of Einstein (field equation) is a fundamental formula.  It specifies gravitational interactions involving energy and mass.  It uses Pi.
Coulomb’s law for electrical force between charges and electrical fields uses Pi.   In magnetism too the magnetic force between poles is expressed in terms of  Pi.

In structural engineering, buckling formula derived by Euler to calculate maximum load on a beam  uses Pi.   In fluid dynamics, viscosity of a fluid is expressed in terms of Pi.   Digital signal processing used in telecommunications extensively,  use formulae involving Pi.  These are used in  filters for eliminating noise in the received signal.

There have been many books on the properties, uses and history of Pi.   In America,  Pi day is celebrated on  March 14th, (3-14).   In some countries  Pi approximation day is celebrated on  22nd July (22/7). 
There are some memorization competitions for children in remembering and reciting the digits of pi.
Some other definition of  Pi  is  the smallest positive integer for which Sine is 0 ,  or that Cosine of  twice Pi  is 0.

In Egypt during 15th century BC Pi was calculated and used as (16/9)^2.  In Babylon during 1900 - 1600 BC , Pi was treated as 25/8.   In India too, during 600 BC in the ancient Vedic  ganith (sulabh) Sutras have treated Pi as (9785/5568)^2.    It seems that in 150 BC Indian mathematics  used Pi as square root of 10 (=3.1622).
A good algorithm to measure Pi geometically using polygons was devised by Greek Mathematician Archimedes during 250 BC.  So Pi is called Archimedes constant.   He drew 96 sided polygons above and below a circle to measure the perimeter and found that  223/71  < pi < 22/7.

Greek Roman scientists Ptolemy found the value to be 3.1416.    In china too values for Pi were found as square root of 10 = 3.1556.   Liu Hui calculated Pi with 3,072 sided polygon using Archimedes algorithm, as 3.1416.

Indian famous Astronomer and mathematician, whom we credit the discovery of 0, has found Pi to be 3.1416 in his  work “Aryabhatiya”  during 499 AD.    Fibonacci – a famous mathematician, calculated in 1220 the value of Pi as 3.1418.

An infinite series for computing Pi was written vedic mathematics (Sanskrit) by Indian Astronomer Nilakantha Somayaji  in Tantrasangraha  in 1500 AD.   It was also proved too.  

Pi / 4  = 1 -1/3 + 1/5 -1/7 + 1/9 – 1/11 + 1/13 -1/15 +…..    is the Madhava’s  formula, which was rediscovered by many European mathematicians.
An very good approximation to Pi  is given by a simple formula, that matches upto 100 digits of Pi.  It is by John Machin in 1706.        Pi / 4 = 4 Tan^-1 (1/5)  -  tan^-1 (1/239)

Nilakantha published in 15th century a fast converging series  for pi:
    Pi/4 – 3/4 = 1 /(2*3*4) – 1/ (4*5*6) + 1/(6*7*8) – 1/(8*9*10) + …

It seems we need about 39 digits of Pi to calculate the volume of the known part of the universe with the precision upto  one atom level.

Even Srinivasa Ramanujan  published a number of innovative, simple and elegant  new formulae for Pi.  That formula was used for finding PI upto 17 million digits in 1985.

There is an adventure based English/Hindi  film titled “The life of Pi”  which was released in 2-D and 3-D internationally, featuring a boy whose name is Pi.  
Pi sounds great and grand  to hear. 

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