Aplicacao de determinante: area de poligono convexo e volume de piramide
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Data
2015-06-17
Autores
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Federal de Goiás
Resumo
This work will concentrate on making a rereading of the theories that surround the
procedures for calculating the area of a convex polygon, as well as the volume of a
pyramid whose base is a polygon convex, with its vertices properly represented in a
coordinate system, in the plan or in space, respectively. Addresses some topics on arrays
and determinant and some of its applications, in particular the study of polygon area
and the volume of the pyramid. Based on applying a decisive factor for the calculation
of the area of a triangle with its vertices represented in a coordinate system, presents
a new theorem to calculate the area of any polygon convex, as well as, a new formula
to calculate the volume of any pyramid with convex basis as a direct application of the
volume of the tetrahedron with its vertices represented in an orthogonal system. For
both, it was essential to the concept of coordinates in the plane and in space, vectors in
the plane and in space, and some of its properties, being essential for the demonstrate
the volume of the tetrahedron and the area of the triangle, using determinant.
Keywords: Volume. Area. Convex polygon. Pyramid. Triangle. Tetrahedron
Descrição
Palavras-chave
Volume, Area, Poligno convexo, Piramide, Triangulo, Tetraedro, Determinante, Matriz, Vertice, Sistema ortogonal, Volume, Area, Convex polygon, Pyramid, Triangle, Tetrahedron, Determinant, Matrix, Vertex, Orthogonal system
Citação
Araujo, Elismar Jose de. Aplicacao de determinante: area de poligono convexo e volume de piramide. 2015. 102 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Universidade Federal de Goiás, Catalão, 2015.