A STUDY ON THE RELATIONSHIPS BETWEEN THE SIDES AND ANGLES OF A TRIANGLE, INSERTED IN A LETTER WRITTEN BY AL-BIRUNI, WITH DIRECTIONS TO THE TRAINING OF THE MATHEMATICS TEACHER
History of Islamic mathematics in the 11th century. Al-Biruni's letter to Abu Said. Geometric knowledge. Historic-activities-with-technology. Interface between history and teaching.
Focused on the study of the history of mathematics (HM), more precisely on the history of Islamic mathematics in the medieval period, this work was based on a document written by al-Biruni in the 11th century, which carries at its core an initial greeting, five demonstrations on some relations between sides and angles in triangles on the sphere and in the plane and a final salutation. From the study of this document, we turn to the proposition of an interface between history and teaching through the alliance between HM and digital technologies (DT) via mathematical investigation (IM). Therefore, the present dissertation was guided by the following question: from a pilot application, what refinements can be proposed to a Digital Didactic Guide elaborated based on the didactic potentialities of a letter by al-Biruni in the 11th century? Aiming to answer this question, our general objective is to develop an articulation between the history of mathematics and teaching aimed at the training of mathematics teachers. We emphasize that we combined methodological procedures and different instruments to compose the analyzed data, they are: bibliographic research, documentary research, semi-structured questionnaires, photographs, field diary, filming, recordings and records of participants in the activities proposed with the Educational Product. As a result, we present a refined Educational Product, from an application in the discipline that was carried out in the didactic discipline of mathematics I of the degree in mathematics at the Federal University of Rio Grande do Norte.