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    pi pi Presentation Transcript

    • What is pi
      Pi is the 16th Greek letter which represents perimeter. It is also used to represent the value of circumference / diameter. Its standard value is 22/7 and it is irrational
    • Understanding pi
    • An Egyptian scribe named Ahmes wrote the oldest known text to give an approximate value for π. TheRhind Mathematical Papyrus dates from the Egyptian Second Intermediate Period—though Ahmes stated that he copied a Middle Kingdom papyrus (i.e. from before 1650 BC). In problem 48 the area of a circle was computed by approximating the circle by an octagon. The value of pi is never mentioned or computed however. If the Egyptians knew of pi, then the corresponding approximation was 256/81.
      Ahmes
       
      The Rhind Mathematical Papyrus
    • As early as the 19th century BC, Babylonian mathematicians were using π ≈ 25⁄8, which is about 0.5% below the exact value.
      Babylonian mathematicians
    • The Indian astronomer Yajnavalkya gave astronomical calculations in the Shatapatha Brahmana (c. 9th century BC) that led to a fractional approximation of π ≈ 339⁄108 (which equals 3.13888..., which is correct to two decimal places when rounded, or 0.09% below the exact value).
      The  Indian astronomer Yajnavalkya
      Shatapatha
    • In the third century BC, Archimedes proved the sharp inequalities 223⁄71 < π < 22⁄7, by means of regular 96-gons; these values are 0.02% and 0.04% off, respectively
    • Later, in the second century AD, Ptolemy, using a regular 360-gon, obtained a value of 3.141666...., which is correct to three decimal places.
      PTOLEMY
    • The Chinese mathematician Liu Hui in 263 AD computed π with to between 3.141024 and 3.142708 with inscribe 96-gon and 192-gon; the average of these two values is 3.141864, an error of less than 0.01%. However, he suggested that 3.14 was a good enough approximation for practical purposes. Later he obtained a more accurate result π ≈ 3927⁄1250 = 3.1416.
      LIU HUI
    • Aryabhata worked on the approximation for pi (π), and may have come to the conclusion that π is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes:
      .
      "Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."[10]
      This implies that the ratio of the circumference to the diameter is ((4+100)×8+62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures.
      It is speculated that Aryabhata used the word āsanna (approaching), to mean that not only is this an approximation but that the value is incommensurable (or irrational).
    • Jones was a great mathematician, his most noted contribution is his proposal for the use of the symbol π (the Greek letter pi) to represent the ratio of the circumference of a circle to its diameter.
       
      Portrait of William Jones
    • Al Khawarizmi told that pi was =
      3.1416
      Al Kashi (1430) => computed Pi to 14 places
      Viète (1540- 1603) => 9 places
      Romanus (1561-1615) => 17 places
      Van Ceulen (1600) => 35 places
      Al Khawarizmi
       In 1647, Oughtred used the symbol (d/Pi) for the ratio of the diameter of a circle to its circumference. In 1697,werDavid Gregory used (Pi/r) for the ratio of the circumference of a circle to its radius. The first to use with its present meaning was an Welsh
      Euler adopted the symbol in 1737 and it quickly became a standard notation.
      Al Kashi
      Euler
      Romanus
      Viète
      Van Ceulen
      Oughtred
    • An estimate of π accurate to 1120 decimal digits was obtained using a gear-driven calculator in 1948, by John Wrench and Levi Smith. This was the most accurate estimate of π before electronic computers came into use
      3.1415926535 8979323846 2643383279 5028841971 6939937510
      5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989 3809525720 1065485863 2788659361 5338182796 8230301952 0353018529 6899577362 2599413891 2497217752 8347913151 5574857242 4541506959
    • PI HAS LOT OF USES SOME OF THEM ARE
    • Uses of pi
    • .
      V = (4/3)πR3.
    • Other uses of pi
      • In definite integrals
      • Complex numbers
      • Calculus
      • And more
    • Nobel prize winning poet WisławaSzymborska wrote a poem about π, and here is an excerpt:
      The caravan of digits that is pidoes not stop at the edge of the page,but runs off the table and into the air,over the wall, a leaf, a bird's nest, the clouds, straight into the sky,through all the bloatedness and bottomlessness.Oh how short, all but mouse-like is the comet's tail!
      Many schools around the world observe Pi Day (March 14, from 3.14). At least one cheer at the Massachusetts Institute of Technology includes "3.14159!"
      On November 7, 2005, alternative musician Kate Bush released the album Aerial. The album contains the song "π" whose lyrics consist principally of Bush singing the digits of π to music, beginning with "3.14".
      In Carl Sagan's novel Contact, π played a key role in the story. The novel suggested that there was a message buried deep within the digits of π placed there by the creator of the universe. This part of the story was omitted from the film adaptation of the novel.
      Darren Aronofsky 's film Pi deals with a number theorist.
      The Wheel of Dublin (Ferris wheel) has been nicknamed "the pi in the sky".
    • REPRESENTATIONS OF PI
    • THANK YOU
      LETS CHEER FOR PI,THE MATH GOD