A PROOF OF THE PYTHAGOREAN THEOREM FROM THE POINT OF VIEW OF RAIMUNDO TEIXEIRA MENDES

Abstract

This research is a detailed analysis of the demonstration of the Pythagorean Theorem from the point of view of Teixeira Mendes, according to physical documents that contain two demonstrations of the Pythagorean Theorem, one written by Gustavo A. Silveira and the other by Teixeira Mendes, both transcribed by Arão Reis. The primary source for this analysis was found in the collection of the Museu Casa Benjamin Constant, specifically in the Fundo B.C. Série Instituto Politécnico Brasileiro BC/IPT, REG 533. To achieve this objective, we proceeded as follows: Initially, we thoroughly examined the steps of demonstrating the Pythagoras' theorem present in this historical document. Then, we used the Geogebra tool to construct the figures and recreate the steps from Teixeira Mendes' demonstration. These commented constructions help in the analysis of the document proposed by this Brazilian, since the geometric concepts are visualized in an intuitive way. This study contributes to the enrichment of knowledge about the history of mathematics in Brazil, highlighting the importance of Teixeira Mendes and his unique approach in demonstrating one of the best-known and cited theorems in Euclidean geometry and highlighting the relevance of preserving and studying historical documents, such as those present in the collection of the Casa Benjamin Constant Museum, to understand the development of mathematics in a national context.