Analyzing the flat sections from a projective geometry perspective: a case of homology

Abstract

This work deals with an analysis of plane sections from a perspective of geometric transformations, more precisely Projective Geometry, as a case of Homology. Geometric transformations are operations applied to a certain element - Object - in order to produce another element - Image. Through theoretical contributions, we will present Homology and its elements. We will analyze some plane sections, highlighting the presence of the elements of Homology in the layout to obtain each one. We undertook a bibliographic search of the topic covered in this article, to later investigate the Projectivity present in the plane sections. We take as a basis the works developed by Soares (1962), Costa and Costa (1994) and Melo (1993), which discuss and present the projective theory and / or its relationship with Descriptive Geometry and Conical Perspective. In such an analysis, we will highlight the presence of the elements of homology for the defense that these sections can be taken as a case of Homology. Based on the exposition of the ideas and analyzes carried out, we verified the existence of the elements of Homology in the layout of flat sections, even if omitted or with another name, and which are essential for the realization of graphic representations in general.