Introducció als desenvolupaments de determinades superfícies reglades des de l'anàlisi matemàtica

Abstract

Geometrical bodies determined by developable ruled surfaces such as a cylinder cut by oblique planes, an oblique cone with a circular base, and multiple other intersections of such solid bodies are constantly made present in our everyday lives by several knowledge disciplines such as art, architecture and industrial design. In a wider sense, the applicability of such structures in present society is therefore essential. However, the only available sources of information on the study of such developments are mainly geared to either geometrical construction of the ruler-and-compass nature, or to generating digital images, thus paying no attention to the deduction or explanation of their underlying equations. This is why the main purpose of this article lies in introducing the exploration of such equations and the significant results which derive from them through mathematical analysis, in order to make them more familiar to a wider audience. In this way, both differential geometry and ruler-and-compass geometry, far from excluding one another, complement each other wonderfully, and lead to a better understanding of certain isometric-to-the-plane surfaces.