Transcendental curves by the inverse tangent problem: Historical and didactical insights for calculus

Abstract

In this paper, based on a workshop held at ESU 2022 (Salerno), aimed at secondary school and university teachers, as well as historians and didacticians, we suggest a new approach to calculus from a constructive geometric perspective. Specifically, we will provide a historical presentation of certain geometric instruments related to calculus, and we will introduce a new device for hands-on experiences. After that, we will describe the activities of the workshop presented at the latest ESU 9 in Salerno, in which we alternated the introduction of historical sources and laboratory activities.