Conjugacy and geometry I : foot of the perpendicular, distance and gram determinant
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | , , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.26/46821 |
Resumo: | In this note on space geometry, the Gram determinant is used for expressing distances, vectors whose magnitude equals those distances and best approximation points. Three cases are considered: distances from a point to a line and to a plane and distances between two skew lines. (Symbolic) determinants occur in the expressions of the feet of perpendiculars and in the representation of the vectors materializing the distances. Because best approximation problems often require the use of subspaces, in order to solve the general cases of the proposed problems, we make extensive use of the conjugacy principle much present in Mathematics. The main purpose of this paper, focused on the resolution of distance problems in tridimensional geometry, is to provide the acquisition of spatial abilities through the proposed constructive approach. The obtained results, which could be a starting point and give clues for solving more advanced geometry problems, are applicable in several fields of practical sciences, such as the Coordinate Metrology, for instance. Moreover, this paper may be a window for coming across with a diversity of scalar products. |
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Conjugacy and geometry I : foot of the perpendicular, distance and gram determinantIn this note on space geometry, the Gram determinant is used for expressing distances, vectors whose magnitude equals those distances and best approximation points. Three cases are considered: distances from a point to a line and to a plane and distances between two skew lines. (Symbolic) determinants occur in the expressions of the feet of perpendiculars and in the representation of the vectors materializing the distances. Because best approximation problems often require the use of subspaces, in order to solve the general cases of the proposed problems, we make extensive use of the conjugacy principle much present in Mathematics. The main purpose of this paper, focused on the resolution of distance problems in tridimensional geometry, is to provide the acquisition of spatial abilities through the proposed constructive approach. The obtained results, which could be a starting point and give clues for solving more advanced geometry problems, are applicable in several fields of practical sciences, such as the Coordinate Metrology, for instance. Moreover, this paper may be a window for coming across with a diversity of scalar products.Pushpa Publishing HouseRepositório ComumCosta, CecíliaMartins, Fernando M. L.Serôdio, RogérioTadeu, PedroVincente, M. A. FacasVitória, José2023-09-28T09:53:49Z20092009-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.26/46821enginfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-10-05T02:15:48Zoai:comum.rcaap.pt:10400.26/46821Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:33:18.862627Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Conjugacy and geometry I : foot of the perpendicular, distance and gram determinant |
title |
Conjugacy and geometry I : foot of the perpendicular, distance and gram determinant |
spellingShingle |
Conjugacy and geometry I : foot of the perpendicular, distance and gram determinant Costa, Cecília |
title_short |
Conjugacy and geometry I : foot of the perpendicular, distance and gram determinant |
title_full |
Conjugacy and geometry I : foot of the perpendicular, distance and gram determinant |
title_fullStr |
Conjugacy and geometry I : foot of the perpendicular, distance and gram determinant |
title_full_unstemmed |
Conjugacy and geometry I : foot of the perpendicular, distance and gram determinant |
title_sort |
Conjugacy and geometry I : foot of the perpendicular, distance and gram determinant |
author |
Costa, Cecília |
author_facet |
Costa, Cecília Martins, Fernando M. L. Serôdio, Rogério Tadeu, Pedro Vincente, M. A. Facas Vitória, José |
author_role |
author |
author2 |
Martins, Fernando M. L. Serôdio, Rogério Tadeu, Pedro Vincente, M. A. Facas Vitória, José |
author2_role |
author author author author author |
dc.contributor.none.fl_str_mv |
Repositório Comum |
dc.contributor.author.fl_str_mv |
Costa, Cecília Martins, Fernando M. L. Serôdio, Rogério Tadeu, Pedro Vincente, M. A. Facas Vitória, José |
description |
In this note on space geometry, the Gram determinant is used for expressing distances, vectors whose magnitude equals those distances and best approximation points. Three cases are considered: distances from a point to a line and to a plane and distances between two skew lines. (Symbolic) determinants occur in the expressions of the feet of perpendiculars and in the representation of the vectors materializing the distances. Because best approximation problems often require the use of subspaces, in order to solve the general cases of the proposed problems, we make extensive use of the conjugacy principle much present in Mathematics. The main purpose of this paper, focused on the resolution of distance problems in tridimensional geometry, is to provide the acquisition of spatial abilities through the proposed constructive approach. The obtained results, which could be a starting point and give clues for solving more advanced geometry problems, are applicable in several fields of practical sciences, such as the Coordinate Metrology, for instance. Moreover, this paper may be a window for coming across with a diversity of scalar products. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009 2009-01-01T00:00:00Z 2023-09-28T09:53:49Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.26/46821 |
url |
http://hdl.handle.net/10400.26/46821 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Pushpa Publishing House |
publisher.none.fl_str_mv |
Pushpa Publishing House |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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