A evolução do cálculo de áreas através da história

Abstract

This paper presents a historical study of the evolution of calculation techniques for areas, from antiquity to the seventeenth century. Several results are proofed for areas of Lunes, Arbelos, Salinon, Ellipse, Parabolic Segments, and regions under the graph of functions like f (x) = xn. It is also shown that the area between the cycloid and its basis is three times the area of its generating circle. Combining history of mathematics with using the technology provided by the GeoGebra software, that lets you view the results dynamically, this work could serve as aid to the math teacher, particularly of basic education, because it uses affordable ideas to students to show areas of regions not covered in this grade level.