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- Pi abstract "The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century though it is also sometimes spelled out as "pi" (/paɪ/).Being an irrational number, π cannot be expressed exactly as a common fraction, although fractions such as 22/7 and other rational numbers are commonly used to approximate π. Consequently its decimal representation never ends and never settles into a permanent repeating pattern. The digits appear to be randomly distributed although no proof of this has yet been discovered. Also, π is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straight-edge.For thousands of years mathematicians have attempted to extend their understanding of π, sometimes by computing its value to a high degree of accuracy. Before the 15th century mathematicians such as Archimedes and Liu Hui used geometrical techniques, based on polygons, to estimate the value of π. Starting around the 15th century, new algorithms based on infinite series revolutionized the computation of π. In the 20th and 21st centuries mathematicians and computer scientists discovered new approaches that, when combined with increasing computational power, extended the decimal representation of π to, as of late 2011, over 10 trillion (1013) digits. Scientific applications generally require no more than 40 digits of π so the primary motivation for these computations is the human desire to break records but the extensive calculations involved have been used to test supercomputers and high-precision multiplication algorithms.Because its definition relates to the circle, π is found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses or spheres. It is also found in formulae used in other branches of science such as cosmology, number theory, statistics, fractals, thermodynamics, mechanics and electromagnetism. The ubiquity of π makes it one of the most widely-known mathematical constants both inside and outside the scientific community: Several books devoted to it have been published, the number is celebrated on Pi Day and record-setting calculations of the digits of π often result in news headlines. Attempts to memorize the value of π with increasing precision have led to records of over 67,000 digits.".
- Pi wikiPageExternalLink index.php?id=11&PPN=PPN235181684_0020&DMDID=DMDLOG_0031&L=1.
- Pi wikiPageExternalLink Pi.html.
- Pi wikiPageExternalLink 3029000.
- Pi wikiPageExternalLink 3029832.
- Pi wikiPageExternalLink pi.
- Pi wikiPageExternalLink ?i=Representations+of+Pi.
- Pi wikiPageID "23601".
- Pi wikiPageRevisionID "606753503".
- Pi align "left".
- Pi alt "Needles of length ℓ scattered on stripes with width t".
- Pi alt "Thousands of dots randomly covering a square and a circle inscribed in the square.".
- Pi caption "Buffon's needle. Needles a and b are dropped randomly.".
- Pi caption "Random dots are placed on the quadrant of a square with a circle inscribed in it.".
- Pi direction "horizontal".
- Pi fontsize "100.0".
- Pi fontsize "90.0".
- Pi footer "Monte Carlo methods, based on random trials, can be used to approximate .".
- Pi hasPhotoCollection Pi.
- Pi image "Buffon needle.gif".
- Pi image "Pi 30K.gif".
- Pi qalign "left".
- Pi quote "Initialize : Iterate : : Then an estimate for is given by :".
- Pi quote "The Gauss–Legendre iterative algorithm:".
- Pi width "100".
- Pi width "166".
- Pi subject Category:Complex_analysis.
- Pi subject Category:Mathematical_series.
- Pi subject Category:Pi.
- Pi comment "The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century though it is also sometimes spelled out as "pi" (/paɪ/).Being an irrational number, π cannot be expressed exactly as a common fraction, although fractions such as 22/7 and other rational numbers are commonly used to approximate π.".
- Pi label "Kreiszahl".
- Pi label "Número π".
- Pi label "Pi (wiskunde)".
- Pi label "Pi greco".
- Pi label "Pi".
- Pi label "Pi".
- Pi label "Pi".
- Pi label "Pi".
- Pi label "Пи (число)".
- Pi label "ط (رياضيات)".
- Pi label "円周率".
- Pi label "圓周率".
- Pi sameAs Pí_(číslo).
- Pi sameAs Kreiszahl.
- Pi sameAs Αριθμός_π.
- Pi sameAs Número_π.
- Pi sameAs Pi_(zenbakia).
- Pi sameAs Pi.
- Pi sameAs Pi.
- Pi sameAs Pi_greco.
- Pi sameAs 円周率.
- Pi sameAs 원주율.
- Pi sameAs Pi_(wiskunde).
- Pi sameAs Pi.
- Pi sameAs Pi.
- Pi sameAs m.05wjw.
- Pi sameAs Mx4rvzKZSJwpEbGdrcN5Y29ycA.
- Pi sameAs Q167.
- Pi sameAs Q167.
- Pi wasDerivedFrom Pi?oldid=606753503.
- Pi isPrimaryTopicOf Pi.