Who found the first value of pi and what was its value?
What is the new value of pi and who found it?
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Answers
The first value of pi was 3.1605 and it was founded by archimedes
The new value of pi is 3.14
Hope it helps you..........!!
#S.H.I.E.L.D ™
1) What is PI:
Pi = π = 22/7 (nearly) = 3.14156 approx.
Pi is a mathematical constant. It is precisely defined as the ratio of a circle’s circumference (perimeter) to its diameter. Greek letter π is given by an English mathematician William Jones in early 18th century. But only after mathematician (German) Leonhard Euler used it in his work “Mechanica”, during 1940s, others have accepted the Greek letter.
Pi is a non terminating irrational and transcendental number. 22/7 or 3.14 is only approximate value, for our convenience and easy calculations. It cannot be found as a root or zero of a rational polynomial in algebra; Nor as a nth root of a rational number, for any n.
2) Efforts to find Pi
An ancient challenge of squaring a circle with a compass and ruler (straight edge) is not solvable. The task is to draw a square with area equal to Pi, starting from a circle of radius 1.
Chinese and Indians calculated pi to 5 digits by the 5th century CE. BrahmaGupt calculated pi using geometrical means. In the 14th century, Madhava discovered Madhava-Leibniz series to find pi.
With computers, educational institutes and enthusiasts computed pi to large number of digits. In 2014, pi is computed to 13 trillion digits and it had taken a few months do that.
3) USES of PI:
Pi is mainly useful in geometry, science & maths. It is part of even cosmology, number theory, trigonometry, probability distributions, complex numbers, statistics, thermodynamics, mechanics, electromagnetism (Coulomb's law). Computations of areas and volumes of circular, elliptical, spherical, cylindrical objects are all based on Pi.
Simple pendulum‘s time period is calculated using Pi, length of the pendulum and gravity. In Quantum mechanics, Heisenberg’s uncertainty principle 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 using Pi.
Coulomb’s law for electrical force between charges and electric fields uses Pi. 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 (telecommunications) uses formulae with Pi. These are used in filters for eliminating noise in the received signal.
4) Credits to Pi:
There are 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).
5) More Calculations of Pi
Another 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).
An algorithm to measure Pi geometrically 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 scientist Ptolemy found the value to be 3.1416. In China too values for Pi were found as √10=3.1556. Liu Hui calculated Pi with 3,072 sided polygon using Archimedes algorithm, as 3.1416.
Indian famous Astronomer & mathematician, whom we credit the discovery of 0, has found Pi to be 3.1416 in his work “Aryabhatiya” (Aryabhatta) 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 again 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.
Great Srinivasan 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.
6) Thanks to Pi
An adventure based English/Hindi film “The life of Pi” was released in 2-D and 3-D internationally, featuring a boy whose nickname is Pi.
Pi sounds great and grand to see, write and hear.