O Tratado Aritmético de al-Khwarizm e o cálculo no quadro de areia (Tahkt)

Suzie Maria de Albuquerquerque; Bernadete Barbosa Morey

doi:10.22481/intermaths.v6i1.16977

Authors

Suzie Maria de Albuquerquerque Universidade Federal do Rio Grande do Norte, Natal-RN, Brasil https://orcid.org/0000-0002-2531-0385
Bernadete Barbosa Morey Universidade Federal do Rio Grande do Norte, Natal-RN, Brasil https://orcid.org/0000-0003-3253-0383

DOI:

https://doi.org/10.22481/intermaths.v6i1.16977

Keywords:

Sand Board, Indian Arithmetics, al-Khwarizmi’s Arithmetical Treatise, History of Mathematics

Abstract

We named The Arithmetical Treatise as the work written by the Islamic scholar al-Khwarizmi, who lived and worked in ninth-century Baghdad under the patronage of Caliph al-Ma'Mum (813–833). The treatise presents an exposition of arithmetic based on the positional and decimal numeral system used by the Indians. During our study of the treatise, we discovered an artifact utilized by Islamic scholars to perform arithmetic operations involving erasure. This artifact, known as the Sand Board, is the focal point of this article, which aims to highlight the calculation processes associated with its use and explore its potential applications in elementary school classrooms and initial teacher training programs.

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References

L. Radford e G. SANTI, “Learning as a critical encounter with the other: prospective teachers conversing with the history of mathematics”. ZDM Mathematics Education 54, 1479–1492. 2022.

S. M. de Albuquerque, “Um estudo histórico-epistemológico e matemático do Tratado Aritmético de al-Khwarizm”. Orientadora: Dra. Bernadete Barbosa Morey. 2024. 125f. Tese (Doutorado em Ensino de Ciências e Matemática) - Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Natal, 2024.

Al-Khwarizm. “Мухаммад ибн Муса ал-Хорезми: Книга об индийском снете” (Trad. A.P. Yushkiévirch). In: Академии наук Узбекской ССР С.Х. СИРАЖДИНОВ (Editor) .Мухаммад ибн Муса аль-Хорезми: Трактаты по математике. Издательство «Фан» Узбекской ССР: Москва, 1983, p. 5-19.

B. A. Bulgakov e B. Rozenfeld. “Эпоха, жизнь и окружение”. In: B. A. Bulgakov, ROSENFELD, A. P. Rozenfeld e A. A. Akhmedov, Мухаммад ал-Хорезми. Editora Nauka, 1983.p. 8-52.

K. Volgel, “Mohammed ibn Musa Alchwarizmis: algorismus, das früheste Lehrbuch zum Rechnen mit indischen Ziffern Nach der einzigen (lateinischen) Handschrift” (Cambridge Un. Lib. Ms. I i. 6. 5.) in Faksimile mit Transkription und Kommentar herausgegeben. Otto Zeller Verlagsbuchhandlung: Aalen, 1963.

M. Folkers, “Die älteste lateinische Schrift über das indische Rechnen nach al- Kwharizmı”. Edition, Übersetzung und Kommentarvon M. Folkerts unter Mitarbeit von Paul Kunitzsch. München:Bayerische Akademie der Wissenschaften, Philosophisch-historische Klasse, Abhandlungen, NeueFolge, 1997.

A. P. Yushkiévitch, “Мухаммад ибн Муса аль-Хорезми: Трактаты по математике. [примечания к переводу]”. Издательство «Фан» Узбекской ССР: Москва, 1983.

Al-Uqlidisi. “Kitab AL-fusul fi AL-hisab AL-hindi”. In: SAIDAN, A. S. The arithmetic of Al-Uqlidisi: the story of hindu-arabicaritmétic as told in Kitab al-fusul fi al-hisab al- híndi. 1 ed. Boston: Reidel Publishing Company, 1978.

A. P. Yushkiévirch, “Арифметический Трактат Mухаммеда Бен Муса ал-Xорезми”. In: A. P. YUSHKIÉVITCH (Editor). Труды института истории естествознания и техники. Академия Наук ССtooСР: Москва, 1954, p. 85-127.

A. S. Saidan, “The arithmetic of Al-Uqlidisi: the story of hindu-arabic aritmétic as told in Kitab al-fusul fi al-hisab al-híndi”. 1. ed. Boston: Reidel Publishing Company, 1978.

Al-Nasawi. “Абу-л-Хасан Али ибн Ахмад ан-Насави” (Tradução do árabe por M. I. Medovoy, notas de M. I. Medovoy com a participação de B. A. Rosenfeld. Достаточное об индийской арифметике. In: RYBKIN, G. F; YUSHKIÉVITCH, A. P. (Editores). Историко-математические исследования. Государственное издательство физико-математической литературы: Мокба, 1963, p. 8-52. Medovoi e Rozenfeld (1960, tradução do al-Nasawi)

Brasil. Ministério da Educação. “Base Nacional Comum Curricular”. Brasília, 2018.

Radford, L. “Teoria da objetivação: uma perspectiva Vygotskiana sobre conhecer e vir a ser no ensino e aprendizagem da matemática”. São Paulo: Livraria da Física, 2021 (Tradução de B. Morey e S. Gobara).