
Pi  Wikipedia, the free encyclopedia

Pi  Wikipedia, the free encyclopedia
The first such representation was the Viète's formula, ..... a b A001203: Continued fraction for Pi, OnLine Encyclopedia of Integer Sequences ...
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Viète's Nested Square Root Representation of Pi  Wolfram ...

Pi  Wolfram Demonstrations Project
Viète's Nested Square Root Representation of Pi · Approximating Pi with ... Approximations of Pi · Geometric Mean of Continued Simple Fraction Terms ...
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Math History
Viete used decimals in this work, but wrote them differently to how we now write them. ... for 100 000 times pi, the number we would write as 314 159.26535. .... He was also the first to use the term "continued fraction," although ...
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A history of [pi] (pi)  Google Books Result
Petr Beckmann  1971  Mathematics  200 pages
Petr Beckmann holds up this mirror, giving the background of the times when pi made progress  and also when it did not, because science was being stifled by ...
books.google.com/books?isbn=0312381859...  
Machin's Formula

Ken's blog: Pi formulae

Mathematical Constants
Viete's formula for pi. and Isaac Newton used 22 terms of this series to find pi .... whose numbers are the Fibonacci numbers Continued fractions and the ...
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Reading Classics Home Page
Pascal Desargues Wallis Viete Kepler Lord Brouncker Galileo Huygens ... reciprocal squares is pi^2/6; Sam Fotis: Continued fractions and the Riccati equation ... Euler: On the transformation of infinite series into continued fractions ...
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The Story of Pi  ResonancePub.Com
H. Havermann, Simple Continued Fraction Expansion of Pi. ... F. Viète, Variorum de Rebus Mathematicis Reponsorum Liber VIII, 1593; Pi: A Source Book, pp. ...
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CRC concise encyclopedia of mathematics  Google Books Result
Eric W. Weisstein  2003  Mathematics  3242 pages
Ogilvy, CS "Pi and PiMakers." Ch. 10 in Excursions in Mathematics. New York: Dover, pp. 108120, 1994. Olds, CD Continued Fractions. ...
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PlanetMath: pi

Online Encyclopedia and Dictionary  Pi
Pi is also known as Archimedes' constant (not to be confused with Archimedes' number) and .... π has many continued fractions representations, including: ...
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數 學資料庫  數學趣趣地  數學文章
and substituting x=Pi/2 , he get. Equation. After Viète, John Wallis (1616 ... (1620  1684) turned this product into the first continued fraction of p: ...
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PI, FOURIER TRANSFORM AND LUDOLPH VAN CEULEN
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by M Vajta  Related articles  All 10 versions
number of new algorithms in the form of infinite series, products or continued fractions possible. François. Viète, a lawyer and amateur mathematician, ...
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The geometric period
... (this value is one of the partial quotients of the continued fraction of Ö3). .... 1579 : François Viète (15401603, France): 9 digits with a polygon of ... [8]: H.C. Schepler, The Chronology of Pi, Mathematics Magazine, (1950) ...
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References
[31]: J.M. Borwein and P.B. Borwein, Pi and the AGM  A study in ... [40]: R.P. Brent, Computation of the regular continued fraction for Euler's constant, Math. ..... [210]: F. Viète, Opera Mathematica (reprinted), Georg Olms Verlag, ...
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The history of pi
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1593 François Viète finds first infinite product to describe pi. 1593 Adrian Romanus finds pi to 15 ... 1655 Brouncker converts it to a continued fraction. ...
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Pi, a source book  Google Books Result
Lennart Berggren, Jonathan M. Borwein, Peter B ...  2004  Science  797 pages
Viete. Variorum de Rebus Mathematicis ... continued fraction expression for 4/ pi. 12. Huygens. De Circuli Magnitudine Inventa (1654) 81 Huy gens' s ...
books.google.com/books?isbn=0387205713...  
pi
Note that this continued fraction is not periodic. Pi or π is a .... The first such representation was the Viète's formula, found by François Viète in 1593. ...
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The Life of Pi  From des to ENIAC and Beyond
Of course 22/7 is one of the early continued fraction approximations to π. .... Pi's Adolescence. The dawn of modern mathematics appears in Vieta's or ...
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The Number $\pi$, Pierre Eymard, Book  Barnes & Noble
2.1, Viete's infinite product, 44 ... 2.11, Continued fractions for [pi], 65. 2.12, The formula of Bailey, Borwein and Plouffe, 79 ...
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A PI, Len Berggren, Book  Barnes & Noble
9 Viète. Variorum de Rebus Mathematicis Reponsorum Liber VII (1593) .... of the irrationality of pi is based on a complicated continued fraction expansion. ...
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Pi: Facts, Discussion Forum, and Encyclopedia Article
The first such representation was the Viète's formula, ..... Pi and continued fraction. The sequence of partial denominators of the simple continued ...
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a general treatise  BooNet Personal Accounts, your ISP serving MD ...
And Brouncker transformed that into a continued fraction 4/pi = 1 + 1ý ...... 1593 Francois Viete finds pi as an infinite irrational product composed of an ...
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Wapedia  Wiki: Pi

Piunleashed:  Google Books Result
Jörg Arndt, Christoph Haenel  2001  Computers  270 pages
Francois Viete (15401603) developed the first infinite product for 2/7r in ... 16201684) made his mark in 1658 with the first ever continued fraction for ...
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What does pi equal?  Yahoo! Answers
5 Dec 2007 ... Continued fraction. Note that this continued fraction is not periodic. .... The first such representation was the Viète formula, ...
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What is pi?  Yahoo! Answers
1 The letter pi 2 Definition 3 Properties 4 Formulae 4.1 Geometry 4.2 Analysis 4.3 Continued fractions 4.4 Number theory 4.5 Dynamical systems and ergodic ...
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Viete biography
Viète continued to serve Henry IV in Paris until 1597 when he went back to his .... Extract from Works (printed 1609) showing the use of decimal fractions. ... History Topics: Pi through the ages · History Topics: A chronology of pi ...
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Mathematical Chronology
Shen Kua writes Meng ch'i pi t'an (Dream Pool Essays), which is a work on mathematics, .... Viète begins publishing the Canon Mathematicus which he intends as a mathematical .... Brouncker gives a continued fraction expansion of 4/π . ...
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Pi  from Wolfram MathWorld
Gosper, R. W. Table of Simple Continued Fraction for pi .... Viète, F. Uriorum de rebus mathematicis responsorum, liber VIII, 1593. Wagon, S. "Is pi Normal? ...
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Pi Formulas  from Wolfram MathWorld
in terms of the inverse tangents of unit fractions is Machin's formula ..... Vieta (1593) was the first to give an exact expression for pi by taking n=4 ...
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The Chronology of PI
by HC Schepler  1950  Cited by 14  Related articles  All 3 versions
Francois Vieta (15401603) (Paris, France). Between 3.1415926535 .... the Royal Society, who brought it into the form of a continued fraction: ...
www.jstor.org/stable/3029832  
THE MATHEMATICAL GAZE'II'E The last chapter is devoted to a study ...
by S Abbott  2000
divisibility, continued fractions and 'cleavages'. BUD WINTER1DGE .... A publication like Pi: a source book therefore has two advantages: firstly, ... The new edition includes translations of the Latin papers (by Viete and ...
www.jstor.org/stable/3620800   [PDF]
Contents
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Viète. Variorum de Rebus Mathematicis Reponsorum Liber VII (1593) 53. Two excerpts. ... Brounker's continued fraction expression for 4/pi. 12. Huygens. ...
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Formulas
[Wallis, late 1600s]; 4/Pi = 1+1/(2+32/(2+52/(2+72/(2+... continued fraction. ... [François Viète, late 1500s] Significance: First infinite expression for ...
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Viete
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StateMaster  Encyclopedia: Pi
François Viète, 1593 (proof). frac{sqrt2}2 cdot frac{sqrt{2+sqrt2}}2 ..... The continued fraction representation of π can be used to generate successively ...
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The History of Pi  Department of Mathematics, Texas A&M University
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The French mathematician Francois Vieta (15401603), the first .... He proves this using a continued fraction expansion of e given by Euler in ...
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Greatest Mathematicians born between 400 and 1580 A.D.
He also did work with continued fractions, trigonometry, and geometry. ... Francois Viete (or Franciscus Vieta) was a French nobleman and lawyer who was a ... PI := 2 Y := 0 LOOP: Y := SQRT(Y + 2) PI := PI * 2 / Y IF (more precision ...
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Using Metode Roseta Nusantara can determine various constants ...
http://www.courses.fas.harvard.edu/~fs5/pi/M8TechTree/Vieta's%20Product.mcd .... fractions and then form the new fraction, we get the correct answer. ...
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The story of pi  Gresham College  Lectures and Events
17 Jan 2007 ... New approaches were given by Francois Viète and John Wallis, who obtained infinite ... This approach was continued by others: for example, ... it cannot be written as a fraction a/b, where a and b are whole numbers. ...
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PI, FOURIER TRANSFORM AND LUDOLPH VAN CEULEN

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Thomas J. Osler
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[Copied from http://www.glue.umd.edu/~jasonp/piref.txt on 10/7/98 ...
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Why is Pi a magic number. It crops up all over mathematics ...
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But the history of Pi, (i.e. the history of maths), is a mirror of the history of Man. .... at one point I think he asks, "How many Newtons have died in Viet Nam? ... I wish more information about continued fractions and...more An ...
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In the sixteenth century, Francois Vieta of Paris found pi to nine decimal ... but nevertheless, mathematicians continued to calculate pi to more and more decimal places. ... Or as the infinite fraction: = ( )( )( )( )( )( )( )( )… ...
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29 Jul 2004 ... Of course 22/7 is one of the early continued fraction .... The dawn of modern mathematics appears in Vieta's or Viéte's product (1579) ...
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The Math Forum  Math Library  Number Theory
... Fibonacci, Vieta, conic sections, mathematics at Princeton ...more>> ... its multiples and powers, continued fractions, formulae, and numerical relations ... A complete history of pi, with resources for teachers for anything from ...
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Transcendental vs. Algebraic Numbers
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Euler also gave the continued fraction expansions of e and noticed a pattern, ... Egyptian and Mesopotamian values of pi were estimated by 25/8 = 3.125 (2, pg 1) ... Viete in late 1500s to 9 places. Roomen in 1600s to 17 places ...
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Fourier Transform and Ludolph van Ceulen
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Downloadable Papers

lC(s) D'(s)i
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Composite number for pi satisfies Euler's equation.
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ABSTRACTS
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Pascal's triangleand Bernoulli's and Vieta's. Mathematical. Spectrum 20(2), 3337. ... Pi Mu Epsilon celebrates 75 years of mathematical activity. Pi Mu .... On parts of parts and ascending CONTINUED FRACTIONS: An investigation of ...
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Pi: Encyclopedia II  Pi  Numerical approximations of π
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Mathematical Chronology.
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John Wallis  New World Encyclopedia
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Is there any nonrecreational mathematics about the Golden Ratio ...
19 Dec 2009 ... On the other hand, e and pi are so fundamental to everything in math; .... The golden ratio has a particularly nice continued fraction ...
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Mathematical Recreations And Essays  Table of Contents from ...
Geometrical fallacies; Geometrical paradoxes; Continued fractions and lattice ... and Diocles; Solutions by Vieta, Descartes, Gregory of St. Vincent, and Newton ... Geometrical methods of approximation to the numerical value of Pi ...
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[pi]: the chronicle.  Free Online Library
The eminent French mathematician Francois Vieta finds [pi] correct to nine decimal ... converts the result to a continued fraction con·tin·ued fraction ...
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Best kdigit rational approximation of irrational numbers: Pre ...
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4 Nov 2007 ... The method of Archimedes [5] involves approximating pi by the .... Francois Viete obtained π correct up to nine decimal places. ... The first of these developments is the continued fraction representation for e. ...
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Quasideterminants, I
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and the noncommutative Bezout and Vieta theorems (as a background of non .... objects φi : k〈x〉 → Pi, i = 1,2 are specializations s : P1 → P2, ...... subsection the infinite continued fraction A11 may be written as a ratio of ...
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The operator continuedfraction method is used to solve the problem on the stress ... Using the Vieta theorem for Eq. (1.4) quadratic in u 2, we obtain .... where L 0 (0) is the value of L (0) for a linearly elastic body, and Pi are ...
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Mathematics Pronunciation Guide
continued kuhn 'tin yood continued fraction kuhn 'tin yood 'frak shuhn ...... circumferentia Phrase used for the value of pi before the Greek letter was used. ..... Pierre François Viete 15401603 vee 'et. vigesimal vih 'jes (uh) muhl ...
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Lecture 07
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2 / Pi // N. 0.63662. † Why is Vieta's formula correct? We know that. sinHzL = 2 cosJ ... Consider a continued fraction from the previous lecture ...
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modern notation the simple continued fraction .... R. C. Gupta: “Some Ancient Values of Pi and Their Use in India”, Mathematics. Education, Vol. 9, No. .... Evelyne Barbin, Centre François Viète, Faculté des sciences et des ...
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Diễn đàn Toán học > Bài giảng về Vô tỷ và Siêu việt
 [ Translate this page ]5 posts  3 authorsNext, the theory of continued fraction expansion provided a very useful tool. ... H. Lambert and L. Euler, in the XVIIIth century, for the numbers e and pi. ...
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Earliest Uses of Symbols for Fractions
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Holidayrelated Math « 360
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torus.math.uiuc.edu/cal/math/cal?year=2009...08...  Cached  
History of Mathematics  Education Resource  StudySphere
... interpolation, continued fraction, mantissa, and hypergeometric series. ... We call a formula representing a sum of distinct unit fractions an Egyptian fraction . .... History of PI The value of Pi has a great value in our scientific life, ... computed Pi to 14 places ViÈte (1540 1603) => 9 pl Read More ...
www.studysphere.com/.../MathematicsHistoryofMathematics771.html  Cached  Similar   [PDF]
Problems by Proposer, Number, Topic & Location,
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To: The period of a p,q sequence relating to a continued fraction as its own upper ..... To: Discovering properties of convolutions for VietaFibonacci and Vieta ..... To: Arithmetic progressions of Fibonacci pseudoprimes, PI(1986)253 ...
www.mscs.dal.ca/Fibonacci/GMiscPrbs46474Proc9.pdf   [PPT]
Algebraic Symbolism
File Format: Microsoft Powerpoint  View as HTML
... after the 3rd century BCE but development of math continued in the East. .... Described HinduArabic notation and decimal fractions; Created new symbols. Multiplication x; Proportion :: Pi for circumference (not for ratio ... Changed unknowns from Viete's (a e i o u) to (u v w x y z) –end of alphabet. ...
orion.math.iastate.edu/lhogben/classes/AlgebraicSymbolism.ppt  Similar  
What a melon has to say • Roots of Unity 1 @ MathLinks
We just apply a shift of \pi/n to the angle of each root; that is, a shift of \alpha/n . ... One tool we can apply to it is Vieta's relations between the roots and .... is irrational, we can make a continued fraction expansion to get a ...
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mathematics: Development of Mathematics — Infoplease.com
Decimal fractions were invented by Simon Stevin and logarithms by John ... These developments continued with the group theory of M. S. Lie in the late 19th ...
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Index via Encyclopedic Dictionary of Mathematics System
18 Jan 2000 ... Number Theory [296]; Number Theory, Elementary [297]; Continued Fractions [083] ... Geometric Constructions [179]; Regular Polyhedra [357]; Pi [332] .... Teiji [415]; Viète, François [444]; Von Neumann, John [445] ...
www.math.niu.edu/~rusin/knownmath/index/EDM.html  Cached  Similar 
Feb 8, 2010
viete continued fraction pi  Google Search
http://www.google.com/search?q=viete+continued+fraction+pi&btnG=Google+Search&num=100
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