Bilhar de Poncelet

• Ano de defesa: 2007
• Autor(a) principal: Éden Santana Campos Amorim
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: Bilhar; Matemática; Seções cónicas; Geometria algebrica
• Link de acesso: http://hdl.handle.net/1843/EABA-76XU4Q

In Applications dAnalyse et de G´eom´etrie, 1862, Poncelet presents a work about pairs of conics holding an inscribe polygon at one and simultanealy circunscribe at another. He proves that when there exists a polygon satisfying this property,then there exist infinitely many polygons with the same number of edges satisfying its too. In this work we are interested to study the varieties of pairs of conics related by polygons, particularly triangles. We construct a fibration over a space of configurationsof degenerate triangles and we use it to recover the bidegree of the variety of pairs of conics related by triangles employing techniques of intersection theory.