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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 theses 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 |
Files in This Item:
File | Description | Size | Format | |
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memoria.pdf | Memòria | 1.4 MB | Adobe PDF | View/Open |
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