Pythagorean Theorem: From the school context to professional practice in determining alignments and areas of urban lots

Abstract

When addressing a given subject, teachers often face questions about the origin and purpose of the material presented. Often, due to a lack of in-depth knowledge, they are unable to adequately answer these questions, presenting the content in a manner that is disconnected from its historical and practical context. This article aims to explore the use of the Pythagorean Theorem, from its introduction in elementary school to its application in various professional areas, with an emphasis on Civil Engineering and Architecture. The focus is not only on its theoretical demonstration and calculation of dimensions, but also on its role in the creation of constructive forms developed by engineers and architects. The choice of the Theorem is due to its historical relevance in the development of Mathematics and its applicability in future content in different professions. The study includes a brief historical contextualization of the Theorem, an analysis of its application in elementary school, with practical exercises extracted from textbooks, and an approach applied to civil construction, especially in the delimitation and description of urban and rural areas. The results indicate that the Pythagorean Theorem plays a fundamental role in the graphical representation of property boundaries, helping to define their sides and angles, particularly through the use of the right triangle, an essential figure for determining boundaries and areas in urban and rural subdivision documents.