Visual thinking and simplicity of proof

Detalhes bibliográficos
Autor(a) principal: Cain, Alan J.
Data de Publicação: 2019
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://doi.org/10.1098/rsta.2018.0032
Resumo: The author was supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through an Investigador FCT research fellowship (IF/01622/2013/CP1161/CT0001). This work was partially supported by the Fundacao para a Ciencia e a Tecnologia through the project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes) and the projects PTDC/MHC-FIL/2583/2014 and PTDC/MAT-PUR/31174/2017.
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spelling Visual thinking and simplicity of proofDiagramsSimplicity of proofSpatial thinkingVisual thinkingMathematics(all)Engineering(all)Physics and Astronomy(all)The author was supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through an Investigador FCT research fellowship (IF/01622/2013/CP1161/CT0001). This work was partially supported by the Fundacao para a Ciencia e a Tecnologia through the project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes) and the projects PTDC/MHC-FIL/2583/2014 and PTDC/MAT-PUR/31174/2017.This paper studies how spatial thinking interacts with simplicity in [informal] proof, by analysing a set of example proofs mainly concerned with Ferrers diagrams (visual representations of partitions of integers) and comparing them to proofs that do not use spatial thinking. The analysis shows that using diagrams and spatial thinking can contribute to simplicity by (for example) avoiding technical calculations, division into cases, and induction, and creating a more surveyable and explanatory proof (both of which are connected to simplicity). In response to one part of Hilbert’s 24th problem, the area between two proofs is explored in one example, showing that between a proof that uses spatial reasoning and one that does not, there is a proof that is less simple yet more impure than either. This has implications for the supposed simplicity of impure proofs.CMA - Centro de Matemática e AplicaçõesRUNCain, Alan J.2019-07-10T22:32:18Z2019-03-112019-03-11T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://doi.org/10.1098/rsta.2018.0032eng1364-503XPURE: 11796543http://www.scopus.com/inward/record.url?scp=85061334936&partnerID=8YFLogxKhttps://doi.org/10.1098/rsta.2018.0032info: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:RCAAP2024-03-11T04:34:25Zoai:run.unl.pt:10362/75100Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:35:29.103002Repositório 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 Visual thinking and simplicity of proof
title Visual thinking and simplicity of proof
spellingShingle Visual thinking and simplicity of proof
Cain, Alan J.
Diagrams
Simplicity of proof
Spatial thinking
Visual thinking
Mathematics(all)
Engineering(all)
Physics and Astronomy(all)
title_short Visual thinking and simplicity of proof
title_full Visual thinking and simplicity of proof
title_fullStr Visual thinking and simplicity of proof
title_full_unstemmed Visual thinking and simplicity of proof
title_sort Visual thinking and simplicity of proof
author Cain, Alan J.
author_facet Cain, Alan J.
author_role author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
RUN
dc.contributor.author.fl_str_mv Cain, Alan J.
dc.subject.por.fl_str_mv Diagrams
Simplicity of proof
Spatial thinking
Visual thinking
Mathematics(all)
Engineering(all)
Physics and Astronomy(all)
topic Diagrams
Simplicity of proof
Spatial thinking
Visual thinking
Mathematics(all)
Engineering(all)
Physics and Astronomy(all)
description The author was supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through an Investigador FCT research fellowship (IF/01622/2013/CP1161/CT0001). This work was partially supported by the Fundacao para a Ciencia e a Tecnologia through the project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes) and the projects PTDC/MHC-FIL/2583/2014 and PTDC/MAT-PUR/31174/2017.
publishDate 2019
dc.date.none.fl_str_mv 2019-07-10T22:32:18Z
2019-03-11
2019-03-11T00:00:00Z
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 https://doi.org/10.1098/rsta.2018.0032
url https://doi.org/10.1098/rsta.2018.0032
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1364-503X
PURE: 11796543
http://www.scopus.com/inward/record.url?scp=85061334936&partnerID=8YFLogxK
https://doi.org/10.1098/rsta.2018.0032
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.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
instname_str 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)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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