fractions, continued fractions bookmarks

Page consacrée aux fractions égyptiennes

PAGES WEB

<http://mathworld.wolfram.com/ContinuedFraction.html>

Continued fraction representations

The Wolfram Functions Site was created as a resource for the educational, mathematical, and scientific communities. (Wolfram Research, Inc.)

<http://functions.wolfram.com/ElementaryFunctions/Power/10/>

Numerical Analysis

I. Introduction. II. An algorithm: continued fractions III. Rational functions/ power series expansion in continued fractions

Web site on elementary physics and different ways of looking at life.

<http://mpec.sc.mahidol.ac.th/numer/>

Simple Continued Fraction Expansion of Pi

<http://www.total.net/~haver/cfpi.html>

Algorithms for Egyptian Fractions

<http://www.ics.uci.edu/~eppstein/numth/egypt/intro.html>

Egyptian mathematics papyri

There are two primary sources and a number of secondary sources on Egyptian Mathematics. The primary sources are the Rhind (or Ahmes) Papyrus and the Moscow Papyrus, and between them they contain 112 problems with solutions. Among the secondary sources are three payri from ~1800 BC: Egyptian Mathematical Leather Roll (a table of 26 decompositions of unit fractions); the Berlin Papyrus (two problems of simultaneous equations - one of the 2nd degree); the Reisner Papyrus (volume calculations).

<http://newton.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egyptpapyrus.html>

Fractions continues

Gilles Bannay

La gamme un peu de theorie : Rappel de physique, Physiologie de l'oreille, Harmoniques et timbres, ProblÃ¨me de la gamme, Fractions continues, 1ere 2eme 3eme 4eme approx.

<http://gilles.bannay.free.fr/>

An Introduction to the Continued Fraction

Dr Ron Knott

<http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/cfINTRO.html>

PAGES PERSONNELLES - HOME PAGES

Hans Havermann - Rarebit Dreams

Continued Fraction of ...

<http://www.total.net/~haver/>

LOGICIELS - SOFTWARES

Contfrac

<http://contfrac.sourceforge.net/>

Constructive reals OCaml library

ValÃ©rie MÃ©nissier-Morain L'arithmÃ©tique exacte , La preuve formelle mÃ©canisÃ©e , Le calcul formel certifiÃ© , La qualitÃ© des calculs flottants

<http://www.lri.fr/~filliatr/creal.en.html>

Concert de musique microtonale
Abbaye du Thoronet

JAVASCRIPT

DÃ©veloppement en fractions continues

Jean-Paul Davalan

Le nombre positif X dont on cherche le dÃ©veloppement en fraction continue est donnÃ© sous la forme d'une fraction A/B ou d'un nombre dÃ©cimal D.

<http://perso.wanadoo.fr/jean-paul.davalan/arit/frcont/index.html>

THÉORIE - THEORY

Continued Fraction Arithmetic

Bill Gosper

<http://www.tweedledum.com/rwg/cfup.htm>

SUJETS - SUBJECTS

Chaos in Numberland: The secret life of continued fractions

by John D. Barrow

<http://pass.maths.org/issue11/features/cfractions/index.html>

DOCUMENTS - PAPERS

Egyptian Fractions

Egyptian Fractions Kevin Gong UC Berkeley Math 196 Spring 1992

<http://kevingong.com/Math/EgyptianFractions.pdf>

Fractions continues : Ã©tude d'un algorithme sur une surface de Veech

T. LeliÃ¨vre 2 oct. 2001

Fractions continues classiques, fractions continues au plus proche entier, propriÃ©tÃ©s, th. de LÃ©vy. InterprÃ©tations gÃ©omÃ©triques. surface de Veech (octogone rÃ©gulier dont on a identifiÃ© les cÃ´tÃ©s opposÃ©s)

<http://cermics.enpc.fr/~lelievre/rapports/Veech.ps>

1998-5 B. LECLERC, On certain formulas of Karlin and SzegÃ¶

Some identities due to Karlin and SzegÃ¶ which provide a relationship between determinants of classical orthogonal polynomials of Wronskian and Hankel type are shown to be specializations of a general algebraic identity between minors of a matrix.

karsze3.ps (DÃ©veloppements en fractions continues de certaines fonctions)

(N'a rien Ã voir avec les fractions continues : erratum du livre " LOGIQUES, ENSEMBLES, CATÃGORIES. Le point de vue constructif." que j'ai lu et que je recommande vivement).

<http://www.math.unicaen.fr/~ageron/rcSDAD.html>

Fractions continues

On the connexion of quaternions with continued fractions and quadratic equations

William Rowan Hamilton 1853

<http://www.emis.de/classics/Hamilton/PRIAQCF.pdf>

On Shanks' algorithm for computing the continued fraction of log_b a

Terence Jackson, Keith Matthews

We give a more practical variant of Shanks' 1954 algorithm for computing the continued fraction of log_b a, for integers a > b > 1, using the floor and ceiling functions and an integer parameter c > 1. The variant, when repeated for a few values of c = 10^r, enables one to guess if log_b a is rational and to find approximately r partial quotients.

<http://www.cs.uwaterloo.ca/journals/JIS/VOL5/Jackson/matthews3.html>

Code and pseudo code

I. Vardi Mathematica Journal (1996)

<http://www.lix.polytechnique.fr/Labo/Ilan.Vardi/pseudo_code.ps>

Continued fractions

Beeler, M., Gosper, R.W., and Schroeppel, R. HAKMEM. MIT AI Memo 239, Feb. 29, 1972. Retyped and converted to html ('Web browser format) by Henry Baker, April, 1995.

ITEM 101B (Gosper): Continued Fraction Arithmetic

Continued fractions let us perform numerical calculations a little at a time without ever introducing any error, such as roundoff or truncation. As if this weren't enough, the calculations provide automatic error analysis, and obviate most forms of successive approximation. This means we can start with an arithmetic expression like sqrt(3/pi^2 + e) / (tanh(sqrt(5)) - sin(69)) and immediately begin to produce the value as a sequence of continued fraction terms (or even decimal digits, if we should be so reactionary), limited only by time and storage...

<http://www.inwap.com/pdp10/hbaker/hakmem/cf.html>

Exact Real Computer Arithmetic with Continued Fractions

Jean Vuillemin INRIA 1987

<http://hal.inria.fr/docs/00/07/57/92/PDF/RR-0760.pdf>

COURS - COURSES

Fractions continues

M. Couchouron

Les documents sont disponibles au format pdf

<http://agreg-maths.univ-rennes1.fr/documentation/Complements.html>

BIOGRAPHIES

Lord William Brounker (1620 - 1684)

De formation linguistique et philosophique (doctorat en 1647 Ã Oxford) et fondateur avec Wallis de la Royal Society, William Brounker se passionne nÃ©anmoins pour les mathÃ©matiques. Sur la demande de son ami Wallis, il entreprend des recherches sur et les fractions continues, ce qui lui permet de proposer le dÃ©veloppement de /4 sous cette forme d'aprÃ¨s la formule de Wallis.

<http://membres.lycos.fr/bgourevitch/mathematiciens/brounker/brounker.html>

Serge Mehl ChronoMath

<http://serge.mehl.free.fr/chrono/Stevin.html>