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THE NUMBER PI( π )

THE NUMBER PI( π ). Andrea Gudelj, Odjel za matematiku Osijek, lipanj, 2013. A brief history about PI. Egyptians and the Babylonians knew about the existence of the constant ratio pi Before the 15th century, Archimedes and Liu Hui – geometry

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THE NUMBER PI( π )

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  1. THE NUMBER PI(π) Andrea Gudelj, Odjel za matematiku Osijek, lipanj, 2013.

  2. A brief history about PI • Egyptians and the Babyloniansknew about the existence of the constant ratio pi • Before the 15th century, Archimedesand Liu Hui– geometry • 15th century, new algorithms based on infinite series

  3. A brief history about PI • 20th century – the developmet of computerrevolutionized the hunt for digits of π • After 1980 – iterative algorithmswere widely used

  4. What is pi actually? • a mathematical constant that is the ratio of a circle's circumferenceto its diameter • an irrational and transcendental number • has been represented by the Greek letter "π" since the mid-18th century

  5. can be represented by an infinite series of nested fractions – continued fraction

  6. Approximate decimal value: • 3.1415926535897932384626433832795028841971693993751058209749445923 0781640628620899862803482534211706798214808651328230664709384460 9550582231725359408128481117450284102701938521105559644622948954 9303819644288109756659334461284756482337867831652712019091456485 6692346034861045432664821339360726024914127372458700660631558817 4881520920962829254091715364367892590360011330530548820466521384 1469519415116094330572703657595919530921861173819326117931051185 4807446237996274956735188575272489122793818301194912983367336244 0656643086021394946395224737190702179860943702770539217176293176 7523846748184676694051320005681271452635608277857713427577896091 7363717872146844090122495343014654958537105079227968925892354201 9956112129021960864034418159813629774771309960518707211349999998 3729780499510597317328160963185950244594553469083026425223082533 4468503526193118817101000313783875288658753320838142061717766914 7303598253490428755468731159562863882353787593751957781857780532 171226806613001927876611195909216420198 ...

  7. Used in... • Geometry and trigonometry • Statistic, fractals, thermodynamics, mechanics, cosmology, ...

  8. Outside the science • Memorizing digits of pi (pipshilology) • Many schools in the United States observe Pi Day on 14 March

  9. “Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number pi.”William L. Schaaf, Nature and History of Pi

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