Sèries circulars i el porisma d'Steiner

Abstract

[en] In this work, we will study projective geometry mainly in the plane, beginning by giving structure of projective line to a conic so we can work with projectivities on conics. This is useful to prove theorems such as Desargues’ theorem for pencils of conics. We will also be studying metric projective geometry which will allow us to dicuss about circles, orthogonality, angles, etc. in the projective plane. This will be used to on one hand, study classical results such as Euler’s circle and, on the other hand, to prove a more advanced result, Steiner’s porism. To see this theorem, algebraic geometry is generally used but on this project we will study it under the projective geometry framework.