IsisCB Explore

Article ID: CBB183440774

Note sur l'extraction de la racine carrée d'un entier chez ibn Al-Hayṯam et comparaison avec Al-Baġdādī (2021)

Hamouda, Leïla (Author)
Hachaichi, Yassine (Author)

Arabic Sciences and Philosophy
Volume: 31
Issue: 1
Pages: 149-157

URI: http://www.cambridge.org/core/journals/arabic-sciences-and-philosophy/article/note-sur-lextraction-de-la-racine-carree-dun-entier-chez-ibn-alhaytam-et-comparaison-avec-albagdadi/FF737B6C92157E2D4998E269F5AD2FC0

DOI: 10.1017/S0957423920000119

Outside Links

WorldCat

Google Scholar

JSTOR

Academia.edu

Algebra Geometry Numbers Algorithms Mathematics Medieval Ibn al-Haytham, Abū ʿAlī al-Ḥasan Al-Baghdādī, Muwaffaq al-Dīn Muḥammad ʿAbd al-Laṭīf ibn Yūsuf

Dans le cadre des algorithmes numériques introduits et élaborés par les mathématiciens arabes, à partir du ixe siècle, figure l'algorithme de l'extraction de la racine carrée d'un entier naturel. Cet algorithme a été étudié chez plusieurs d'entre eux et surtout bien expliqué par alBaġdādī (mort vers 1037) dans le chapitre « Comment extraire la racine des nombres entiers » de son livre « La complétion du calcul », Al-takmila fī al-ḥisāb 1. Dans ce chapitre, al-Baġdādī expose son travail pédagogiquement en six sections traitant de plusieurs manières différentes le problème de l'extraction de la racine carrée d'un entier 2. À la même époque, dans un texte isolé intitulé « Sur la cause de la racine, de son doublement et de son déplacement 3 », Ibn al-Hayṯam (mort vers 1040) donne une justification géométrique de l'algorithme en se basant sur des notions algébriques précises.As part of the numerical algorithms introduced and developed by Arab mathematicians from the ninth century onwards, there is the algorithm for extracting the square root of a natural number. This algorithm was studied by several of them and especially well explained by alBaġdādī (died around 1037) in the chapter “How to extract the root of whole numbers” from his book “The completion of calculation”, Al-takmila fī al- ḥisāb 1. In this chapter, al-Baġdādī exposes his work pedagogically in six sections dealing in several different ways with the problem of extracting the square root of an integer 2. At the same time, in an isolated text entitled "On the cause of the root, its doubling and its displacement 3”, Ibn al-Hayṯam (died around 1040) gives a geometric justification of the algorithm based on precise algebraic notions.

...More

Citation URI

https://data.isiscb.org/isis/citation/CBB183440774/

Citations Indexes

Similar Citations

Article Charlotte-V. Pollet; (2020)
The Procedure of the Section of Pieces of Areas in Li Ye and Yang Hui’s Works: Genealogy of Diagrams and Equations (/isis/citation/CBB466865729/)

Chapter Ilana Wartenberg; (2012)
The Place of Ibn al-Ahdab's Epistle of the Number in the Diffusion of Arabic Mathematics in Hebrew in Medieval Europe (/isis/citation/CBB906698085/)

Book Rahman, Shahid; (2008)
Unity of Science in the Arabic Tradition: Science, Logic, Epistemology and Their Interactions (/isis/citation/CBB000951507/)

Book Rashed, Roshdi; (2000)
Les mathématiques infinitésimales du IXe au XIe siècle: théorie des coniques, constructions géométriques et géométrie pratique. Vol. 3: Ibn al-Haytham (/isis/citation/CBB000774771/)

Article Johansson, Bo Göran; (2011)
Cube Root Extraction in Medieval Mathematics (/isis/citation/CBB001036222/)

Article Jens Hoyrup; (2018)
Explicit and Less Explicit Algorithmic Thinking, 1200-1500. Jordanus de Nemore, and the Contrast between Barthelemy de Romans et Chuquet (/isis/citation/CBB729622687/)

Article Roshdi Rashed; (2019)
IBN AL-HAYTHAM, IBN SĪNĀ, AL-ṬŪSĪ : ÉGALITÉ OU CONGRUENCE (/isis/citation/CBB521388295/)

Article Rashed, Roshdi; (2012)
L'angle de contingence: Un problème de philosophie des mathématiques (/isis/citation/CBB001220532/)

Thesis Welsh, Whitney Elizabeth; (2011)
Unthinkable: Mathematics and the Rise of the West (/isis/citation/CBB001560636/)

Chapter Hélène Bellosta; (2012)
La destinée arabe des Données d’Euclide (/isis/citation/CBB209738412/)

Article Corry, Leo; (2013)
Geometry and Arithmetic in the Medieval Traditions of Euclid's Elements: A View from Book II (/isis/citation/CBB001213490/)

Book Franco Purini; (2024)
La sezione aurea (/isis/citation/CBB839358183/)

Book Paolo Zellini; (1999)
Gnomon. Una indagine sul numero (/isis/citation/CBB253354203/)

Book Paolo Zellini; (2010)
Numero e logos (/isis/citation/CBB843348217/)

Article Norman Biggs; (2021)
Linear Programming from Fibonacci to Farkas (/isis/citation/CBB910977328/)

Article Álvarez Polo, Yolima; Español González, Luis; (2012)
Algoritmos algebraicos lineales en el primer libro de texto (1917) de Julio Rey Pastor (/isis/citation/CBB001260003/)

Essay Review Michel, Alain; (2003)
Géométrie et philosophie: De Thābit ibn Qurra à ibn al-Haytham (/isis/citation/CBB000340511/)

Article Helen Elizabeth Ross; Betty Irene Knott; (2019)
Dicuil (9th Century) on Triangular and Square Numbers (/isis/citation/CBB215002916/)

Article Fabio Bellissima; (2011)
L'antanairesi e la teoria armonica greca (/isis/citation/CBB718056038/)

Article Yusta, Piedad; (2008)
Geometry in Mesopotamia and Genesis of Algorithms (/isis/citation/CBB000953453/)

Comments

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}