Article ID: CBB183440774

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

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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.

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Authors & Contributors
Rashed, Roshdi
Zellini, Paolo
Michel, Alain P.
Rahman, Shahid
Yusta, Piedad
Johansson, Bo Göran
Journals
Arabic Sciences and Philosophy
Archive for History of Exact Sciences
Bollettino di Storia delle Scienze Matematiche
Historia Scientiarum: International Journal of the History of Science Society of Japan
Historia Mathematica
Llull: Revista de la Sociedad Española de Historia de las Ciencias y de las Técnicas
Publishers
Edizioni Cadmo
Adelphi
Al-Furqan Islamic Heritage Foundation
Springer
Duke University
Concepts
Mathematics
Geometry
Algebra
Arab/Islamic world, civilization and culture
Algorithms
Philosophy of mathematics
People
Ibn al-Haytham, Abū ʿAlī al-Ḥasan
Euclid
Avicenna
ibn Qurra, Thabit
Ptolemy
Ibn Khaldun
Time Periods
Medieval
Ancient
11th century
10th century
9th century
20th century, early
Places
Mesopotamia
Europe
Middle and Near East
Mediterranean region
Spain
Babylon (extinct city)
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