Jean Pierre Demailly

Jean-Pierre Demailly

Description

On the computational complexity of mathematical functions Jean-Pierre Demailly Institut Fourier, Universite de Grenoble I & Academie des Sciences, Paris (France) November 26, 2011 KVPY conference at Vijyoshi Camp Jean-Pierre Demailly (Grenoble I), November 26, 2011 On the computational complexity of mathematical functions

• decimal numeral


• computational complexity


• academie des sciences


• vijyoshi camp


• evaluations used polygon


• chinese mathematicians

Sujets

• Demailly
• Computational Complexity
• Académie des sciences
• Chinese mathematics

Informations

• Publié par: pefav
• Nombre de lectures: 16
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Jn-eaylG(amliereDiPrevemb),NobleIrenoocehtnO1102,62replomlcnaioatutmpflactcnusnoi

November 26, 2011 KVPY conference at Vijyoshi Camp

InstitutFourier,Universit´edeGrenobleI &Acade´miedesSciences,Paris(France)

On the computational complexity of mathematical functions

itexfmyoheattima

Jean-Pierre Demailly

nsioctun

Babylonian mathematical tablet allowing the computation of 2 (1800 – 1600 BC)

Decimal numeral system invented in India (∼500BC ?) :

nalcatioexitompltaehoymfacflamit oCnrecnocg,inutmpldyoerav nore(GlyilmaDerereiP-naeJmputheco1Ont,201re62evbm,)oNlbIe

Madhava’sofmrlufaroπ eiP-naeJenGry(llaiemeDrrpmocixelitatlanoatemalicoftythmavomeeb2rboel)IN,thecompu6,2011Onontincfu

Early calculations ofπwere done by Greek mathematicians several centuries BC.

and Indian

s

ierran-PJenebo(yrGiallDeme6,r2beemov,NI)leatupmocehtnO1102itnolaocpmelixytofmathematicalfuitcnsno

Early calculations ofπwere done by Greek and Indian mathematicians several centuries BC. These early evaluations used polygon approximations and Pythagoras theorem. In this way, using 96 sides, Archimedes got3 + 1 7 0 1 < π <3 + 10 70 whose average is31418(c. 230 BC). Chinese mathematicians reached 7 decimal places in 480 AD.

roπva’sadhaulafformM

’avahdaMlamuorsfrπfo ,)oNevbmeronlbIemailly(GPierreDeJ-nae

The next progress was the discovery of the firstinfinite series formula by Madhava (circa 1350 – 1450), a prominent mathematician-astronomer from Kerala (formula rediscovered in the XVIIe century by Leibniz and Gregory) :

Early calculations ofπwere done by Greek and Indian mathematicians several centuries BC. These early evaluations used polygon approximations and Pythagoras theorem. In this way, using 96 sides, Archimedes got3 + 10 71 < π <3 + 10 70 whose average is31418(c. 230 BC). Chinese mathematicians reached 7 decimal places in 480 AD.

unctcalf

Convergence is unfortunately very slow, but Madhava was able to improve convergence and reached in this way 11 decimal places.

4 π = 1− 3 + 1 5 1 − 1 7 + 1 9 − 1 11 +   ( + 2n −)1 1+ +  

n +  

ionsoymfxetiamittaehioatutmpplomlcna102,62reocehtnO1