Discovering geometry via the Discover command in GeoGebra Discovery

Detalhes bibliográficos
Autor(a) principal: Kovács, Zoltán
Data de Publicação: 2021
Tipo de documento: Artigo
Idioma: por
Título da fonte: Rematec (Online)
Texto Completo: http://www.rematec.net.br/index.php/rematec/article/view/51
Resumo: We present a new way to discover statements in a planar geometric figure by using GeoGebra Discovery, an experimental version of GeoGebra, the free dynamic mathematics software package. A new command "Discover" (which is also available as a tool) requires an input point of the figure---as output several properties of the figure are communicated by the program. That is, "Discover" reports a list of the observed geometric properties, including point equality, equal long segments, collinearity, concyclicity, parallelism and perpendicularity. All of the obtained statements are checked symbolically: this means that the verification is done with computer algebra means. The obtained properties are also highlighted with colors or dashed lines in the original figure. The discovery process can always be continued by creating new objects and selecting a new target point to discover. We focus on possible uses in a classroom: two basic examples are shown from an Austrian textbook first. Then some more difficult topics are introduced that are usually covered by the secondary school curriculum. As a final example, we consider the discovery of a more advanced theorem, namely, a proposition according to Napoleon. In the paper we give some references to related software systems and the applied mathematical background as well.
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spelling Discovering geometry via the Discover command in GeoGebra DiscoveryGeoGebraDiscoveryPlanar GeometryProving StatementsWe present a new way to discover statements in a planar geometric figure by using GeoGebra Discovery, an experimental version of GeoGebra, the free dynamic mathematics software package. A new command "Discover" (which is also available as a tool) requires an input point of the figure---as output several properties of the figure are communicated by the program. That is, "Discover" reports a list of the observed geometric properties, including point equality, equal long segments, collinearity, concyclicity, parallelism and perpendicularity. All of the obtained statements are checked symbolically: this means that the verification is done with computer algebra means. The obtained properties are also highlighted with colors or dashed lines in the original figure. The discovery process can always be continued by creating new objects and selecting a new target point to discover. We focus on possible uses in a classroom: two basic examples are shown from an Austrian textbook first. Then some more difficult topics are introduced that are usually covered by the secondary school curriculum. As a final example, we consider the discovery of a more advanced theorem, namely, a proposition according to Napoleon. In the paper we give some references to related software systems and the applied mathematical background as well.Grupo de Pesquisa Práticas Socioculturais e Educação Matemática2021-01-18info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://www.rematec.net.br/index.php/rematec/article/view/5110.37084/REMATEC.1980-3141.2021.n37.p14-25.id313REMATEC; v. 16 n. 37 (2021); 14-252675-19091980-3141reponame:Rematec (Online)instname:Universidade Federal do Pará (UFPA)instacron:UFPAporhttp://www.rematec.net.br/index.php/rematec/article/view/51/50Copyright (c) 2021 REMATECinfo:eu-repo/semantics/openAccessKovács, Zoltán2022-11-17T22:37:56Zoai:ojs2.www.rematec.net.br:article/51Revistahttp://www.rematec.net.br/index.php/rematecPUBhttp://www.rematec.net.br/index.php/rematec/oairevistarematec@gmail.com||revistarematec@gmail.com2675-19091980-3141opendoar:2022-11-17T22:37:56Rematec (Online) - Universidade Federal do Pará (UFPA)false
dc.title.none.fl_str_mv Discovering geometry via the Discover command in GeoGebra Discovery
title Discovering geometry via the Discover command in GeoGebra Discovery
spellingShingle Discovering geometry via the Discover command in GeoGebra Discovery
Kovács, Zoltán
GeoGebra
Discovery
Planar Geometry
Proving Statements
title_short Discovering geometry via the Discover command in GeoGebra Discovery
title_full Discovering geometry via the Discover command in GeoGebra Discovery
title_fullStr Discovering geometry via the Discover command in GeoGebra Discovery
title_full_unstemmed Discovering geometry via the Discover command in GeoGebra Discovery
title_sort Discovering geometry via the Discover command in GeoGebra Discovery
author Kovács, Zoltán
author_facet Kovács, Zoltán
author_role author
dc.contributor.author.fl_str_mv Kovács, Zoltán
dc.subject.por.fl_str_mv GeoGebra
Discovery
Planar Geometry
Proving Statements
topic GeoGebra
Discovery
Planar Geometry
Proving Statements
description We present a new way to discover statements in a planar geometric figure by using GeoGebra Discovery, an experimental version of GeoGebra, the free dynamic mathematics software package. A new command "Discover" (which is also available as a tool) requires an input point of the figure---as output several properties of the figure are communicated by the program. That is, "Discover" reports a list of the observed geometric properties, including point equality, equal long segments, collinearity, concyclicity, parallelism and perpendicularity. All of the obtained statements are checked symbolically: this means that the verification is done with computer algebra means. The obtained properties are also highlighted with colors or dashed lines in the original figure. The discovery process can always be continued by creating new objects and selecting a new target point to discover. We focus on possible uses in a classroom: two basic examples are shown from an Austrian textbook first. Then some more difficult topics are introduced that are usually covered by the secondary school curriculum. As a final example, we consider the discovery of a more advanced theorem, namely, a proposition according to Napoleon. In the paper we give some references to related software systems and the applied mathematical background as well.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-18
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
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dc.identifier.uri.fl_str_mv http://www.rematec.net.br/index.php/rematec/article/view/51
10.37084/REMATEC.1980-3141.2021.n37.p14-25.id313
url http://www.rematec.net.br/index.php/rematec/article/view/51
identifier_str_mv 10.37084/REMATEC.1980-3141.2021.n37.p14-25.id313
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv http://www.rematec.net.br/index.php/rematec/article/view/51/50
dc.rights.driver.fl_str_mv Copyright (c) 2021 REMATEC
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2021 REMATEC
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Grupo de Pesquisa Práticas Socioculturais e Educação Matemática
publisher.none.fl_str_mv Grupo de Pesquisa Práticas Socioculturais e Educação Matemática
dc.source.none.fl_str_mv REMATEC; v. 16 n. 37 (2021); 14-25
2675-1909
1980-3141
reponame:Rematec (Online)
instname:Universidade Federal do Pará (UFPA)
instacron:UFPA
instname_str Universidade Federal do Pará (UFPA)
instacron_str UFPA
institution UFPA
reponame_str Rematec (Online)
collection Rematec (Online)
repository.name.fl_str_mv Rematec (Online) - Universidade Federal do Pará (UFPA)
repository.mail.fl_str_mv revistarematec@gmail.com||revistarematec@gmail.com
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