The Mathematics behind the chord scale contained in the Sector by John Worgan (1697)

Detalhes bibliográficos
Autor(a) principal: Silva Junior, Francimar Miguel da
Data de Publicação: 2022
Outros Autores: Santos, Andressa Gomes dos, Pereira, Ana Carolina Costa
Tipo de documento: Artigo
Idioma: por
Título da fonte: Educação Matemática Debate
Texto Completo: https://www.periodicos.unimontes.br/index.php/emd/article/view/5120
Resumo: This article aims to present the Mathematics involved in the construction of the string scale inscribed in the mathematical instrument, sector, exposed in John Worgan's 1697 treatise A short treatise of the description of the sector. Worgan's sector has nine scales, namely: equal lines, sines, tangents, secants, polygons, artificial numbers, artificial sines, artificial tangents, and chords. The last one is used to solve problems of a geometric nature, mainly to find angles and divide the circumference into equal parts. As a research methodology, a descriptive qualitative approach was used, using historical documents as the main source of consultation. Its construction allows the development of some geometric knowledge that can help in the understanding of concepts, such as radius, diameter, arc of circumference, angle and chord, among others, for Basic Education students.
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spelling The Mathematics behind the chord scale contained in the Sector by John Worgan (1697)Las Matemáticas detrás de la escala de cuerdas contenidas en el Sector por John Worgan (1697)A Matemática por trás da escala das cordas contida no Setor de John Worgan (1697)Escala das CordasConceitos GeométricosSetor de WorganInstrumentos MatemáticosChord ScaleGeometric ConceptsWorgan SectorMathematical InstrumentsEscala de CuerdasConceptos GeométricosSetor de WorganInstrumentos MatemáticosThis article aims to present the Mathematics involved in the construction of the string scale inscribed in the mathematical instrument, sector, exposed in John Worgan's 1697 treatise A short treatise of the description of the sector. Worgan's sector has nine scales, namely: equal lines, sines, tangents, secants, polygons, artificial numbers, artificial sines, artificial tangents, and chords. The last one is used to solve problems of a geometric nature, mainly to find angles and divide the circumference into equal parts. As a research methodology, a descriptive qualitative approach was used, using historical documents as the main source of consultation. Its construction allows the development of some geometric knowledge that can help in the understanding of concepts, such as radius, diameter, arc of circumference, angle and chord, among others, for Basic Education students.Este artículo tiene como objetivo presentar las Matemáticas involucradas en la construcción de la escala de cuerdas inscrita en el instrumento matemático, sector, expuesto en el tratado de John Worgan de 1697 Un breve tratado de la descripción del sector. El sector de Worgan tiene nueve escalas, a saber: líneas iguales, senos, tangentes, secantes, polígonos, números artificiales, senos artificiales, tangentes artificiales y cuerdas. Este último se utiliza para resolver problemas de carácter geométrico, principalmente para encontrar ángulos y dividir la circunferencia en partes iguales. Como metodología de investigación se utilizó un enfoque cualitativo descriptivo, utilizando documentos históricos como principal fuente de consulta. Su construcción permite el desarrollo de algunos conocimientos geométricos que pueden ayudar en la comprensión de conceptos como radio, diámetro, arco de circunferencia, ángulo y cuerda, entre otros, para los estudiantes de Educación Básica.Este artigo tem como objetivo apresentar a Matemática envolvida na construção da escala das cordas inscrita no instrumento matemático Setor, exposto no tratado A short treatise of the description of the sector, de John Worgan, de 1697. O Setor de Worgan possui nove escalas, a saber: das linhas iguais, dos senos, das tangentes, das secantes, dos polígonos, dos números artificiais, dos senos artificiais, das tangentes artificiais e das cordas. A última é utilizada para a resolução de problemas de natureza geométrica, principalmente, para encontrar ângulos e dividir a circunferência em partes iguais. Como metodologia de pesquisa, fez-se uso de uma abordagem qualitativa descritiva, utilizando documentos históricos como fonte principal de consulta. Sua construção possibilita o desenvolvimento de alguns conhecimentos geométricos, que podem auxiliar na compreensão de conceitos, tais como raio, diâmetro, arco de circunferência, ângulo e corda, entre outros, para alunos da Educação Básica.Editora Unimontes2022-09-16info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://www.periodicos.unimontes.br/index.php/emd/article/view/512010.46551/emd.v6n12a15Educação Matemática Debate; v. 6 n. 12 (2022): jan./dez.; 1-162526-6136reponame:Educação Matemática Debateinstname:Universidade Estadual de Montes Claros (UNIMONTES)instacron:UNIMONTESporhttps://www.periodicos.unimontes.br/index.php/emd/article/view/5120/5953https://www.periodicos.unimontes.br/index.php/emd/article/view/5120/5762https://creativecommons.org/licenses/by-nc-sa/4.0/deed.pt_BRinfo:eu-repo/semantics/openAccessSilva Junior, Francimar Miguel daSantos, Andressa Gomes dos Pereira, Ana Carolina Costa2024-03-27T15:13:30Zoai:ojs2.periodicos.unimontes.br:article/5120Revistahttps://www.periodicos.unimontes.br/index.php/emdPUBhttps://www.periodicos.unimontes.br/index.php/emdrevista.emd@unimontes.br||2526-61362526-6136opendoar:2024-03-27T15:13:30Educação Matemática Debate - Universidade Estadual de Montes Claros (UNIMONTES)false
dc.title.none.fl_str_mv The Mathematics behind the chord scale contained in the Sector by John Worgan (1697)
Las Matemáticas detrás de la escala de cuerdas contenidas en el Sector por John Worgan (1697)
A Matemática por trás da escala das cordas contida no Setor de John Worgan (1697)
title The Mathematics behind the chord scale contained in the Sector by John Worgan (1697)
spellingShingle The Mathematics behind the chord scale contained in the Sector by John Worgan (1697)
Silva Junior, Francimar Miguel da
Escala das Cordas
Conceitos Geométricos
Setor de Worgan
Instrumentos Matemáticos
Chord Scale
Geometric Concepts
Worgan Sector
Mathematical Instruments
Escala de Cuerdas
Conceptos Geométricos
Setor de Worgan
Instrumentos Matemáticos
title_short The Mathematics behind the chord scale contained in the Sector by John Worgan (1697)
title_full The Mathematics behind the chord scale contained in the Sector by John Worgan (1697)
title_fullStr The Mathematics behind the chord scale contained in the Sector by John Worgan (1697)
title_full_unstemmed The Mathematics behind the chord scale contained in the Sector by John Worgan (1697)
title_sort The Mathematics behind the chord scale contained in the Sector by John Worgan (1697)
author Silva Junior, Francimar Miguel da
author_facet Silva Junior, Francimar Miguel da
Santos, Andressa Gomes dos
Pereira, Ana Carolina Costa
author_role author
author2 Santos, Andressa Gomes dos
Pereira, Ana Carolina Costa
author2_role author
author
dc.contributor.author.fl_str_mv Silva Junior, Francimar Miguel da
Santos, Andressa Gomes dos
Pereira, Ana Carolina Costa
dc.subject.por.fl_str_mv Escala das Cordas
Conceitos Geométricos
Setor de Worgan
Instrumentos Matemáticos
Chord Scale
Geometric Concepts
Worgan Sector
Mathematical Instruments
Escala de Cuerdas
Conceptos Geométricos
Setor de Worgan
Instrumentos Matemáticos
topic Escala das Cordas
Conceitos Geométricos
Setor de Worgan
Instrumentos Matemáticos
Chord Scale
Geometric Concepts
Worgan Sector
Mathematical Instruments
Escala de Cuerdas
Conceptos Geométricos
Setor de Worgan
Instrumentos Matemáticos
description This article aims to present the Mathematics involved in the construction of the string scale inscribed in the mathematical instrument, sector, exposed in John Worgan's 1697 treatise A short treatise of the description of the sector. Worgan's sector has nine scales, namely: equal lines, sines, tangents, secants, polygons, artificial numbers, artificial sines, artificial tangents, and chords. The last one is used to solve problems of a geometric nature, mainly to find angles and divide the circumference into equal parts. As a research methodology, a descriptive qualitative approach was used, using historical documents as the main source of consultation. Its construction allows the development of some geometric knowledge that can help in the understanding of concepts, such as radius, diameter, arc of circumference, angle and chord, among others, for Basic Education students.
publishDate 2022
dc.date.none.fl_str_mv 2022-09-16
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://www.periodicos.unimontes.br/index.php/emd/article/view/5120
10.46551/emd.v6n12a15
url https://www.periodicos.unimontes.br/index.php/emd/article/view/5120
identifier_str_mv 10.46551/emd.v6n12a15
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://www.periodicos.unimontes.br/index.php/emd/article/view/5120/5953
https://www.periodicos.unimontes.br/index.php/emd/article/view/5120/5762
dc.rights.driver.fl_str_mv https://creativecommons.org/licenses/by-nc-sa/4.0/deed.pt_BR
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/4.0/deed.pt_BR
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Editora Unimontes
publisher.none.fl_str_mv Editora Unimontes
dc.source.none.fl_str_mv Educação Matemática Debate; v. 6 n. 12 (2022): jan./dez.; 1-16
2526-6136
reponame:Educação Matemática Debate
instname:Universidade Estadual de Montes Claros (UNIMONTES)
instacron:UNIMONTES
instname_str Universidade Estadual de Montes Claros (UNIMONTES)
instacron_str UNIMONTES
institution UNIMONTES
reponame_str Educação Matemática Debate
collection Educação Matemática Debate
repository.name.fl_str_mv Educação Matemática Debate - Universidade Estadual de Montes Claros (UNIMONTES)
repository.mail.fl_str_mv revista.emd@unimontes.br||
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