Using GeoGebra for correction of incorrect premises in geometric proofs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23420%2F19%3A43957071" target="_blank" >RIV/49777513:23420/19:43957071 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.isres.org/books/Erhmst2019_24-12-2019.pdf" target="_blank" >https://www.isres.org/books/Erhmst2019_24-12-2019.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Using GeoGebra for correction of incorrect premises in geometric proofs

Popis výsledku v původním jazyce

Various mathematical statements and their proofs are an integral part of mathematics. Even at elementary schools, pupils get acquainted with simpler ones. An example of such a statement is, for example, the geometric (image) proof of the Pythagorean theorem. However, when performing a geometric proof, respectively. performing a mathematical proof in a geometric way, it is necessary to pay attention to some inaccurate simplifications or erroneous assumptions that may arise in this procedure. Some of these inconveniences can be in part eliminated by appropriate use of dynamic geometry software that offers interactivity and work with dynamic figures instead of static sketches. In this paper, we present a number of such erroneous statements and evidence, supplemented by an explanation where an error occurred in the sequence of logical considerations. Each of the examples is then made correct by performing the appropriate construction in GeoGebra.

Název v anglickém jazyce

Using GeoGebra for correction of incorrect premises in geometric proofs

Popis výsledku anglicky

Various mathematical statements and their proofs are an integral part of mathematics. Even at elementary schools, pupils get acquainted with simpler ones. An example of such a statement is, for example, the geometric (image) proof of the Pythagorean theorem. However, when performing a geometric proof, respectively. performing a mathematical proof in a geometric way, it is necessary to pay attention to some inaccurate simplifications or erroneous assumptions that may arise in this procedure. Some of these inconveniences can be in part eliminated by appropriate use of dynamic geometry software that offers interactivity and work with dynamic figures instead of static sketches. In this paper, we present a number of such erroneous statements and evidence, supplemented by an explanation where an error occurred in the sequence of logical considerations. Each of the examples is then made correct by performing the appropriate construction in GeoGebra.

Druh

C - Kapitola v odborné knize

CEP obor

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OECD FORD obor

50301 - Education, general; including training, pedagogy, didactics [and education systems]

Projekt

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Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Education Research Highlights in Mathematics, Science and Technology 2019

ISBN

978-605-69854-0-9

Počet stran výsledku

11

Strana od-do

79-89

Počet stran knihy

310

Název nakladatele

ISRES Publishing

Místo vydání

Ames, Iowa, USA

Kód UT WoS kapitoly

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