Wallis's use of innovative diagrams

Autores
Ortiz, Erika Rita
Año de publicación
2018
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
Fil: Ortiz, Erika Rita. Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Secretaría de Posgrado; Argentina.
Fil: Ortiz, Erika Rita. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Mathematical research is best characterized by problem solving activities which make use of a variety of modes of representation. Against this background, my aim is to discuss the epistemic value of diagrammatic representation in problem-solving. To make my point, I consider a case study selected from Wallis's work on the quadrature of conic sections. Wallis's definition of conic sections is given in terms of algebraic equations setting them free from "the embrangling of the cone". This suggests the aim to eliminate figures and other iconic elements with a view to attaining higher level of abstraction but, in Wallis's work, geometric diagrams display relations that can be fruitfully used to calculate arithmetically the area of a figure. The use of displayed relations leads to the formulation of algebraic equations defining curves and it is also what makes room for arithmetical calculations. Accordingly, the notion of a general method of resolution is grounded on properties read off the diagram so that despite Wallis's insistence on algebraic representation -Iargue- diagrams remain essential working tools.
https://www.springer.com/us/book/9783319913759
Fil: Ortiz, Erika Rita. Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Secretaría de Posgrado; Argentina.
Fil: Ortiz, Erika Rita. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Filosofía, Historia y Filosofía de la Ciencia y la Tecnología
Materia
Diagrams
Algebraic equations
Wallis, John
Philosophy of mathematical practice
Nivel de accesibilidad
acceso abierto
Condiciones de uso
Repositorio
Repositorio Digital Universitario (UNC)
Institución
Universidad Nacional de Córdoba
OAI Identificador
oai:rdu.unc.edu.ar:11086/557979
Acceder
id RDUUNC_857cf1779adf1013e0cacca64d7cc7c6
oai_identifier_str oai:rdu.unc.edu.ar:11086/557979
network_acronym_str RDUUNC
repository_id_str 2572
network_name_str Repositorio Digital Universitario (UNC)
spelling Wallis's use of innovative diagramsOrtiz, Erika RitaDiagramsAlgebraic equationsWallis, JohnPhilosophy of mathematical practiceFil: Ortiz, Erika Rita. Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Secretaría de Posgrado; Argentina.Fil: Ortiz, Erika Rita. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Mathematical research is best characterized by problem solving activities which make use of a variety of modes of representation. Against this background, my aim is to discuss the epistemic value of diagrammatic representation in problem-solving. To make my point, I consider a case study selected from Wallis's work on the quadrature of conic sections. Wallis's definition of conic sections is given in terms of algebraic equations setting them free from "the embrangling of the cone". This suggests the aim to eliminate figures and other iconic elements with a view to attaining higher level of abstraction but, in Wallis's work, geometric diagrams display relations that can be fruitfully used to calculate arithmetically the area of a figure. The use of displayed relations leads to the formulation of algebraic equations defining curves and it is also what makes room for arithmetical calculations. Accordingly, the notion of a general method of resolution is grounded on properties read off the diagram so that despite Wallis's insistence on algebraic representation -Iargue- diagrams remain essential working tools.https://www.springer.com/us/book/9783319913759Fil: Ortiz, Erika Rita. Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Secretaría de Posgrado; Argentina.Fil: Ortiz, Erika Rita. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Filosofía, Historia y Filosofía de la Ciencia y la Tecnología2018info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdf978-3-319-91375-9http://hdl.handle.net/11086/557979enginfo:eu-repo/semantics/openAccessreponame:Repositorio Digital Universitario (UNC)instname:Universidad Nacional de Córdobainstacron:UNC2025-09-29T13:43:58Zoai:rdu.unc.edu.ar:11086/557979Institucionalhttps://rdu.unc.edu.ar/Universidad públicaNo correspondehttp://rdu.unc.edu.ar/oai/snrdoca.unc@gmail.comArgentinaNo correspondeNo correspondeNo correspondeopendoar:25722025-09-29 13:43:58.528Repositorio Digital Universitario (UNC) - Universidad Nacional de Córdobafalse
dc.title.none.fl_str_mv Wallis's use of innovative diagrams
title Wallis's use of innovative diagrams
spellingShingle Wallis's use of innovative diagrams
Ortiz, Erika Rita
Diagrams
Algebraic equations
Wallis, John
Philosophy of mathematical practice
title_short Wallis's use of innovative diagrams
title_full Wallis's use of innovative diagrams
title_fullStr Wallis's use of innovative diagrams
title_full_unstemmed Wallis's use of innovative diagrams
title_sort Wallis's use of innovative diagrams
dc.creator.none.fl_str_mv Ortiz, Erika Rita
author Ortiz, Erika Rita
author_facet Ortiz, Erika Rita
author_role author
dc.subject.none.fl_str_mv Diagrams
Algebraic equations
Wallis, John
Philosophy of mathematical practice
topic Diagrams
Algebraic equations
Wallis, John
Philosophy of mathematical practice
dc.description.none.fl_txt_mv Fil: Ortiz, Erika Rita. Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Secretaría de Posgrado; Argentina.
Fil: Ortiz, Erika Rita. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Mathematical research is best characterized by problem solving activities which make use of a variety of modes of representation. Against this background, my aim is to discuss the epistemic value of diagrammatic representation in problem-solving. To make my point, I consider a case study selected from Wallis's work on the quadrature of conic sections. Wallis's definition of conic sections is given in terms of algebraic equations setting them free from "the embrangling of the cone". This suggests the aim to eliminate figures and other iconic elements with a view to attaining higher level of abstraction but, in Wallis's work, geometric diagrams display relations that can be fruitfully used to calculate arithmetically the area of a figure. The use of displayed relations leads to the formulation of algebraic equations defining curves and it is also what makes room for arithmetical calculations. Accordingly, the notion of a general method of resolution is grounded on properties read off the diagram so that despite Wallis's insistence on algebraic representation -Iargue- diagrams remain essential working tools.
https://www.springer.com/us/book/9783319913759
Fil: Ortiz, Erika Rita. Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Secretaría de Posgrado; Argentina.
Fil: Ortiz, Erika Rita. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Filosofía, Historia y Filosofía de la Ciencia y la Tecnología
description Fil: Ortiz, Erika Rita. Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Secretaría de Posgrado; Argentina.
publishDate 2018
dc.date.none.fl_str_mv 2018
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dc.identifier.none.fl_str_mv 978-3-319-91375-9
http://hdl.handle.net/11086/557979
identifier_str_mv 978-3-319-91375-9
url http://hdl.handle.net/11086/557979
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.source.none.fl_str_mv reponame:Repositorio Digital Universitario (UNC)
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reponame_str Repositorio Digital Universitario (UNC)
collection Repositorio Digital Universitario (UNC)
instname_str Universidad Nacional de Córdoba
instacron_str UNC
institution UNC
repository.name.fl_str_mv Repositorio Digital Universitario (UNC) - Universidad Nacional de Córdoba
repository.mail.fl_str_mv oca.unc@gmail.com
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score 13.070432

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