Um estudo sobre o Tratado da Circunferência de al-Kashi (1424)

Abstract

This thesis consists of a qualitative documentary and bibliographical research that makes a mathematical, historical and epistemological study of the Treatise on Circumference (al-Risāla al-Muhītīyya), written by the Islamic scholar al-Kāshī in the year 1424, in Samarkand, Uzbekistan . With this study, we intend to highlight elements of the Treatise on Circumference that present pedagogical potential for use in the classroom. Our theoretical framework comprises the concepts of the Theory of Objectification (TO), elaborated by Luis Radford and in this author's conceptions about the articulation between the history of mathematics and mathematics teaching and the methodology of Analysis of Historical Texts of Mathematics (ATHM), elaborated by Fumikazu Saito and collaborators. The base text for our studies was the Russian translation of the Treatise on Circumference, from which we created a working version in Portuguese. We explored issues outside the referred work, such as its manuscripts and translations, historiographical and contextual aspects. We also explore issues within the treatise such as mathematical and epistemological aspects through a series of studies related to each of the treatise's parts. Through such studies, we show the pedagogical potential of the Treatise on Circumference that can favor its use in the classroom. We exemplify this potential by means of two activities developed according to the Theory of Objectification and the simulation in a mathematical program of obtaining the al-Kāshī approximation for the relation between the length of the circumference and its diameter.