Cálculo de área dos triângulos e quadriláteros: um estudo sobre as fórmulas de Heron e Brahmagupta

Abstract

The present work aims to make a historical analysis of the calculation of areas of triangles and quadrilaterals. Initially, a brief history of mathematics was necessary, more specifically of Geometry in ancient civilizations such as: Mesopotamia, Egypt, India and Greece from Thales of Miletus (c. 624 – 546 B.C.) and Pythagoras (c. 585 – 500 B.C.). In Greece, the areas of plane figures were systematized and recorded in the 13 books of Euclid's Elements. In the 1st century, the mathematician Heron of Alexandria (c.10 – 70 A.D.) came up with a formula to calculate the area of any triangle, requiring only knowledge of its perimeter. In the 7th century, using as a basis the knowledge left by Heron, Brahmagupta (598 – 668) created a formula to determine the area of any quadrilateral when its sides were known. Later, with the advancement of trigonometry, it was found that Brahmagupta's formula was valid only for cyclic or inscribable quadrilaterals.