A Desigualdade triangular e a desigualdade de Jensen

Abstract

his paper deals with two important mathematical inequalities: the triangle inequality and Jensen inequality. It first presents an overview of how the issue of inequality is treated improperly in math books for middle level. Then it is explained what is an inequality, continuing an experiment showing empirical geometry so you can "specifically" to ascertain the veracity of the triangle inequality. Continuing the work, seven are shown demonstrations of triangle inequality. Are then presented with three demonstrations of the Jensen inequality. To perform these demonstrations took knowledge of elementary algebra, Euclidean geometry, geometric constructions, mathematical induction, convex of functions, Cauchy-Schuwarz and several other knowledge. Were listed seven issues of application of the triangle inequality and fifteen Jensen inequality, with the aim of providing the reader with a more accurate perception of how these inequalities can be applied to motivate students' creativity in problem solving.