Superfícies regulares no espaço euclidiano

Abstract

In this work, we will study the regular parameterized surfaces in Euclidean space, whose equations are written in the form F(x, y, z) = 0, where F : R3 → R is a differentiable application. For this, we will analyze these equations and what they show about the superfaces. We will study the spherical superfaces, cylindrical, conical, ruled surfaces, of revolution and quadrics, analyzing the intersections of these surfaces with the axes and coordinate planes, the intersections with planes parallel to the coordinate planes, also using the symmetries with the planes, coordinate axes, and with the origin, besides analyze the extension of the surface along the Euclidean space.