Estudo de projeções com uma proposta de atividades para aplicação no ensino médio

Abstract

The projections study is a classic subject of extreme importance for various Math´s fields. In this context, the present thesis has the main goal to evidence its importance firstly bringing a depth theoretical study about projections and some applications on the numeric analysis through the exposure of interplay methods GMRES and Conjugates Gradients that are based on projections of Krylov subspace. On the second moment with the knowledge acquired in this work it was sought to propose some activities which can be apply on the basic education. It has been elaborated interdisciplinary activities engaging the content of Analytic Geometry with the Physics and Physical Education knowledge fields. It has proposed working the projections in the vectors context in the cartesian plan and also in the rules of soccer offside under the currently context of VAR (Video Assistant Referee) technology that has been assumed for FIFA (International Federation of Association Football) in the last decade. It has been built a concrete material called octant box to accomplish the activities as a result to assist the experiments practice as well as giving encouragement to the students. Such material represents an octant of R3 and it is a source that can be utilized for all Analytic Geometry content.