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Title: Sèries circulars i el porisma d'Steiner
Author: Tomàs Ripollés, Tània
Director/Tutor: Naranjo del Val, Juan Carlos
Keywords: Geometria projectiva
Treballs de fi de grau
Seccions còniques
Geometria analítica
Geometria algebraica
Projective geometry
Bachelor's theses
Conic sections
Analytic geometry
Algebraic geometry
Issue Date: 20-Jun-2019
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.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Juan Carlos Naranjo del Val
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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