Curvatura de cônicas.

Abstract

Through this work, we intend to present the concept of curvature from the algebraic and geometric point of view focusing on the study of conical curves (ellipse, hyperbolas and parabola). To this end, we present a historical approach and then a study on plane curves, culminating in the deduction of the curvature formulas and in its geometrical interpretation using the osculating circle. By emphasizing the conical curves, we derive the ellipse, hyperbolas and parabola curvature, whereas we detail a method for finding the centers of curvatures of these conics using only geometrical procedures. We also address important physical applications of the concept of curvature.