Uma proposta histórico-construtivista dos logaritmos.

Abstract

This work leads to a proposal for the study of logarithms based on the stages of their historical construction, focusing on the need for their ingenious creation and on the study of purely algebraic methods used to develop logarithm tables. We will associate arithmetic progressions with geometric progressions and, through these sequences, we will give a proposal, to a certain extent, original, on how to define logarithms, recovering the historical part of this association and how this was actually done. As a consequence, we will discuss limitations of this association for the conceptualization of logarithms and work with definitions and theorems that will be very important for our proposal. Our approach presents the fundamental principles of the creation of classical logarithms, reclaims the role of arithmetic progressions, geometric progressions and Mathematical Analysis of the real line for the realization of this creation. We close with a proposal for a constructivist classwork, in order to provide the teacher with a work suggestion that will enable the student to have a historical and significant learning about logarithms, through arithmetic progressions and geometric progressions.