Material models of ruled surfaces as witnesses to the development of mathematical teaching

Abstract

Starting from the impact, which the École Polytechnique had on higher educations in Europe, this paper wants to highlight the role of material models especially for teaching mathematics. Models of ruled surfaces play a prominent role in this narrative, since Gaspard Monge, who taught “Géometrie descriptive” in Paris between 1794 and 1816, already used string models to support his lectures. For this reason, we want to trace especially the history of ruled surface models from the late 18th century to the presence. The investigation focuses on persons, used materials and the major topics. It is known that the axiomatization of mathematics lead to a decay of the meaning of material models in the early 20th century. But at the same time, material mathematical models gained relevance in other disciplines like civil engineering and art. We also want to show, how ruled surfaces can be part of current teaching projects.