A Desigualdade triangular e a desigualdade de Jensen

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...

Descripción completa

Detalles Bibliográficos
Autor: Campelo, Alexandre Francisco
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2013
País:Brasil
Institución:Universidade Federal do Ceará (UFC)
Repositorio:Repositório Institucional da Universidade Federal do Ceará (UFC)
Idioma:portugués
OAI Identifier:oai:repositorio.ufc.br:riufc/5784
Acceso en línea:http://www.repositorio.ufc.br/handle/riufc/5784
Access Level:acceso abierto
Palabra clave:Desigualdades (Matemática)
Álgebra
Descripción
Sumario: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.