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The constant is named "p" because "p" is the first letter of the Greek words pe??f??e?a (periphery) and pe??µet??? (perimeter), probably referring to its use in the formula to find the circumference, or perimeter, of a circle. Geometrical Definition : Geometrical Definition p (sometimes written pi) is the ratio of any circle's circumference to its diameter. This is the same value as the ratio of a circle's area to the square of its radius. The ratio C/d is constant, regardless of a circle's size. For example, if a circle has twice the diameter d of another circle it will also have twice the circumference C, preserving the ratio C/d. Arithmetical Definition : Arithmetical Definition p is an irrational number. It cannot be written in the form p/q where p and q are integers. Its decimal representation is non- ending & non- reccuring Decimal Representation : Decimal Representation p’ s Decimal representation is non- terminating and non- recurring. Its Decimal Approximation up to 100 digits is 3.14159265358979323846264338327950288419716939937510 58209749445923078164062862089986280348253421170679…. p can be estimated by drawing a large circle, finding its Diameter & Circumference and dividing them. Now there are soft wares which can find up to a trillion decimal places of p. As of January 2010, the record is almost 2.7 trillion digits History of p : History of p The earliest known usage of p was in the Pyramids of Egypt. The history of p is as old as mathematics itself. It is said that ancient Indians, Babylonians, Egyptians and Greeks knew that the C/d ratio was a little more than 3. Ancient India and p : Ancient India and p Ancient India was very advanced in Mathematics. India has made many important contributions in mathematics including ‘0’. Ancient Indians also knew a lot about p. The Indian text Shatapatha Brahmana gives p as 339/108 ˜ 3.139. Indian Mathematicians & p : Indian Mathematicians & p Many Indian mathematicians have made lot of effort on p. Aryabhatta is a mathematician from India who has Made a lot of experiments on p. Madhava of Sangamagrama has also made huge contributions on p. Madhava was able to estimate p as 3.14159265359, which is correct to 11 decimal places Srinivasa Ramanujan on p : Srinivasa Ramanujan on p In the beginning of the 20th century, the Indian mathematician Srinivasa Ramanujan found many new formulas for p. This formula was used to set several p computing records in the end of the 1980s, including the first calculation of over one billion (1,011,196,691) decimals in 1989. It remains the formula of choice for p calculating software that runs on personal computers Archimedes on p : Archimedes on p Archimedes (287–212 BC) was the first to estimate p. For this he inscribed circles in regular polygons and calculated the outer and inner polygons' respective perimeters. By using 96-sided polygons, he proved that 310/71< p <31/7 .The average of these values is about 3.14185 Major Mathematicians on p : Major Mathematicians on p Other Mathematicians including Ptolemy, Liu Hui, Zu Chongzi etc. gave approximate values to p. In 1424 by the Persian mathematician,Jamshid al-Kashi, who gave an estimate p that is correct to 16 decimal digits. Isaac Newton himself derived a series for p and calculated 15 digits. Memorizing Digits : Memorizing Digits Well before computers were used in calculating p, memorizing a record number of digits had become an obsession for some people. In 2006, Akira Haraguchi, a retired Japanese engineer, claimed to have recited 100,000 decimal places. This, however, has yet to be verified by Guinness World Records. The Guinness-recognized record for remembered digits of p is 67,890 digits, held by Lu Chao, a 24-year-old graduate student from China. It took him 24 hours and 4 minutes to recite to the 67,890th decimal place of p without an error. Use of p : Use of p In Geometry p is used to de operations on Circles, Spheres & Cylinders. Area of Circle= p*r*r Circumference of a circle= 2*p*r p is also used in Trigonometry, Calculus, Physics, Probability etc. p is also used in Geomorphology, Under ideal conditions, the ratio between the actual length of a river and its straight-line from source to mouth length tends to approach p. p in popular culture : p in popular culture p Day (March 14, from 3.14) is observed in many schools. On November 7, 2005, musician Kate Bush released the album Aerial. The album contains the song "p" whose lyrics consist principally of Bush singing the digits of p to music, beginning with "3.14”. In Carl Sagan 's novel Contact, p played a key role in the story. The novel suggested that there was a message buried deep within the digits of p placed there by whoever created the universe. p in popular culture : p in popular culture p ties are also used. p shirts are also out for sale. Even p plates are used. ‘p Poems’Poem- 1 : ‘p Poems’Poem- 1 Why, p! Stop, p! Weird anomalies do behave badly!You, madly conjured, imperfect, strange, numerical,Why do you maintain this facade?In finite time you are barbaric!You do wonders, mesmerize minds!O, do elements numerous have a beautiful meaning- A system isolating all mysteries, solutions for puzzles, chaos, aO snafu apparent in O Universal Concept from believing lies?That there, obstinate in you, O Strange Constant, A Divine Sign O exists is unlikely unlessIs O revealed Something Brilliant, negating belief!In formulas, O, you show yourself in Greek and math as a p forever-O hidden wonders absconded, infinite, in a tiny constant, O, sneakily, rather?Never, I say! Poem- 2 : Poem- 2 A Scientific American's DilemmaHubble saw the universe expanding , Watson and Crick found life's startEinstein sensed relativity , While surgeons transplanted a heart.Electrons exchange and release energy , So Schrödinger's cat can meowSimultaneously its life is lost - Quantum mechanics will say how. Chaos and order are intertwined , Physically, mentally, and more,Maybe matter is vibrating strings , But how could one know for sure?This philosophy called science , Has plausibly progressedBut after a Grand Theory comes about , Can there be any more significant success?And if a Grand Theory were proposed , Unifying all that exists,Would the end of pi be found as well,Or has math become eclipsed? Poem -3 : Poem -3 If I gave you a 3 and a 1,4,1,5 You'd have the start Of the greatest number alive If Pi were reduced To a mere 3 The circles of the world Would be hexagonal, you see What may seem minor Just might be big So grab some pie And do some trig! Slide 21: Thank You By, Deepak.P You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.