The Mathematics behind the chord scale contained in the Sector by John Worgan (1697)
Autor(a) principal: | |
---|---|
Data de Publicação: | 2022 |
Outros Autores: | , |
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 As a research methodology, a descriptive qualitative approach was used, using historical documents as the main source of consultation.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. |
id |
UNIMONTES1_9728ebf8c2ed26287b8ca7dcdf37fc3e |
---|---|
oai_identifier_str |
oai:ojs2.periodicos.unimontes.br:article/5120 |
network_acronym_str |
UNIMONTES1 |
network_name_str |
Educação Matemática Debate |
repository_id_str |
|
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|| |
_version_ |
1797174835041796096 |