Título: | COMPLEXITY IN EUCLIDEAN PLANE GEOMETRY | ||||||||||||
Autor: |
SILVANA MARINI RODRIGUES LOPES |
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Colaborador(es): |
HUMBERTO JOSE BORTOLOSSI - Orientador CARLOS TOMEI - Coorientador |
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Catalogação: | 25/FEV/2003 | Língua(s): | PORTUGUESE - BRAZIL |
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Tipo: | TEXT | Subtipo: | THESIS | ||||||||||
Notas: |
[pt] Todos os dados constantes dos documentos são de inteira responsabilidade de seus autores. Os dados utilizados nas descrições dos documentos estão em conformidade com os sistemas da administração da PUC-Rio. [en] All data contained in the documents are the sole responsibility of the authors. The data used in the descriptions of the documents are in conformity with the systems of the administration of PUC-Rio. |
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Referência(s): |
[pt] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=3279&idi=1 [en] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=3279&idi=2 |
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DOI: | https://doi.org/10.17771/PUCRio.acad.3279 | ||||||||||||
Resumo: | |||||||||||||
Two forms of complexity in Euclidean plane geometry are
considered. In the first one, problems are described
algebraically, and the complexity level is measured
essentially by the degree of a polynomial. As a
consequence, many familiar and general results in geometry
can be proved by inspecting two or three special cases. The
second form uses the syntactic description of a theorem
allowing for a quanti.cation of the complexity in logic
terms (number of quantifiers and atoms in the formula).
Inspired by this approach, some procedures in mechanized
proofs are described. We also present some traditional
groups of operations in geometry which simplify the two
approaches. The study of more advanced techniques in
mathematics sheds new light on standard high school topics.
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