Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/110307
Title: Poncelet's porism
Author: Rojas González, Andrés
Director/Tutor: Naranjo del Val, Juan Carlos
Keywords: Corbes algebraiques
Treballs de fi de grau
Superfícies de Riemann
Automorfismes
Corbes el·líptiques
Teoria de torsió (Àlgebra)
Algebraic curves
Bachelor's thesis
Riemann surfaces
Automorphisms
Elliptic curves
Torsion theory (Algebra)
Issue Date: Jun-2016
Abstract: Given two non-degenerate conics $C$ and $D$ in the complex projective plane $\mathbb{P}^{2}_{\mathbb{C}}$ , consider the following problem: constructing a closed polygon inscribed in $C$ and circumscribed about $D$. Assuming that the polygon may have self-intersections, a first approach to build such a polygon could be the next one. Take an arbitrary point $p_0 \in C$ and choose $l_0$ one of the two tangent lines to $D$ passing through $p_0$. If the line $l_0$ is not tangent to $C$ there exists a point $p_1 \in {C} \cap l_0 $ different from $p_0$. Then, take $l_1 \neq l_0$ the tangent line to $D$ through $p_1$. In a similar way, $l_1$ must intersect $C$ at a point $p_2 \neq p_1$.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Juan Carlos Naranjo del Val
URI: http://hdl.handle.net/2445/110307
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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