GEOMETRY

This course in geometry is organised as follows. The first chapter is devoted to the study of parameterized curves. We begin by recalling some definitions of the characterization of a curve as well as the fundamental properties of the curve. We introduce the length of a curve, it is possible to parameterize a curve
by its length. To explain what this parameterization by the curvilinear abscissa represents, the following equations are introduced through a moving frame, the Frenet frame, which is well adapted to the study of skew curves. We highlight the importance of the concepts, the curvature and torsion of a curve. Second
we are interested in the study of parameterized surfaces: such as regular surfaces and differential elements, and we introduce the following concepts (tangent plane and the normal line, to calculate the integral of a continuous function on a surface, the area of a surface, we use the first fundamental form of the surface
which allows us to calculate the length of a curve drawn on the surface). In the last chapter, we are interested in the notions of affine geometry (affine spaces, barycenters, affine varieties, affine applications, affine frames, and affine transformations).