Pie

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Pie

  1. 1. MADE BY : SHAHEENAFROZX-BKENDRIYA VIDAYALAYASEC :30 GNR
  2. 2.  Lets look at what Pi really is.Some declare that Pi is anedible dessert, usuallycircular, consisting ofsomething sweet enclosedwithin a baked crust
  3. 3. Pi or π is a mathematical constant and a transcendental (andtherefore irrational) real number, approximately equal to3.14159, which is the ratio of a circles circumference to itsdiameter in Euclidean geometry, and has many uses inmathematics, physics, and engineering. It is also known asArchimedes constant (not to be confused with an Archimedesnumber).
  4. 4.  LEIBNITZ (1671) Pi= 4(1/1-1/3+1/5-1/7+1/9-1/11+1/13+...) WALLIS Pi= 2(2/1*2/3*4/3*4/5*6/5*6/7*...) MACHIN (1706) Pi=16(1/5- 1/(3+5^3) +1/(5+5^5) -1/(7+5^7)+...) -4(1/239 -1/(3*239^3) + 1/(5*239^5)-...) SHARP (1717) Pi= 2*Sq.Rt(3)(1-1/3*3 + 1/5*3^2 - 1/7*3^5...) EULER (1736) Pi= Sq.Rt(6(1+1/1^2+1/2^2+ 1/3^2...)) BOUNCKER Pi= 4---1+1---2+9---2+25+...
  5. 5.  Pi is one of the longest numbers evercomputed, second only to “e” anotherIRRATIONAL number with a value of2.718281828459045 …. It never repeats like the decimal values of1/3=.33333… or 5/7=.7142857142857…
  6. 6.  The early Babylonians and Hebrews used three as a value for Pi.Later, Ahmes, an Egyptian found the area of a circle . Down throughthe ages, countless people have puzzled over this same question,“What is Pi?" From 287 - 212B.C. therelived Archimedes, who inscribedin a circle and circumscribedabout a circle, regular polygons.The Greeks found Pi to be relatedto cones, ellipses, cylinders and othergeometric figures.
  7. 7. π can be estimated by computing the perimeters ofcircumscribed and inscribed polygons.
  8. 8. When mathematicians arefaced with quantities whichare hard to compute, they try,at least, to pin them betweentwo other quantities whichthey can compute. TheGreeks were not able to findany fraction for Pi. Today weknow that Pi is NOTa rational number and cannotbe expressed as a fraction.
  9. 9. During the 17th century, analytic geometry and calculus weredeveloped. They had a immediate effect on Pi. Pi was freed from thecircle! An ellipse has a formula for its area which involves Pi (a factknown by the Greeks); but this is also true of the sphere, cycloid arc,hypocycloid, the witch, and many other curves.
  10. 10. It’s curious how certain topics in mathematics show up over and over. Inthe late 1940s two new mathematical streams (electronic computing andstatistics) put Pi on the table again.
  11. 11. The development of high speed electronic computing equipment provideda means for rapid computation. Inquiries regarding the number of Pi’sdigits -- not what the numbers were individually, but how they behavestatistically -- provided the motive for additional research.
  12. 12. The computation of Pi to 10,000 places may be of no direct scientificusefulness. However, its usefulness in training personnel to use computersand to test such machines appears to be extremely important. Thus themysterious and wonderful Pi is reduced to a gargle that helps computingmachines clear their throats.

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