Os aspectos matemáticos relacionados à média geométrica que emergem a partir da manipulação da escala dos números (1623) elaborada por Edmund Gunter com licenciandos em Matemática

Abstract

In view of the studies carried out in order to combine history with the teaching of mathematics through an interface, an updated perspective of historical writing was chosen that uses a historical source to seek resources that can serve as a basis for the development of activities. Aiming to contribute to studies that combine history and teaching in this approach, we chose to investigate a mathematical instrument described in Edmund Gunter's treatise (1581-1626), entitled The description and vse of the Sector, the Crosse-staffe, and other instruments, for such as are studious of Mathematicall practise, in such a way as to appropriate the scale of numbers inscribed in the Cross-staff instrument to didactically explore the notion of geometric mean. Thus, this study has the general objective of knowing the mathematical processes involving the geometric mean that permeated the formation of undergraduates in Mathematics from the handling of the scale of numbers. In this way, the research is characterized as qualitative with a bibliographic and documentary nature, in which a survey was carried out on the themes related to this study, as well as a treatment of the chosen historical source. As for the development of the activity, the support of the Theory of Objectification was used. The contextual sphere was mobilized from the study of the treaty in which the context of the elaboration of Gunter's work was presented. A study was also carried out in the epistemological scope directed to the scale of numbers. The historiographical sphere, on the other hand, permeates the two previous moments. Training was applied with a degree in Mathematics for the perception of mathematical knowledge related to the geometric mean, resulting in the mobilization of knowledge such as logarithm, analytical geometric and algebra associated with the geometric mean. In this way, it contributes to the training of mathematics teachers with the use of resources from history, especially with the scale of numbers for the teaching of geometric mean from articulations with other areas of mathematics.