Construction and exploration of particular curves and evolutes of theirs using GeoGebra dynamic software

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10440215" target="_blank" >RIV/00216208:11320/21:10440215 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Construction and exploration of particular curves and evolutes of theirs using GeoGebra dynamic software

Popis výsledku v původním jazyce

The article deals with the synthetic construction of specific planar curves which are defined by geometric motions and with the modeling of these constructions in GeoGebra dynamic system. We focus on the constructions of trajectories, envelopes, and centers of curvature and osculating circles of specific curves. We present a par- ticular construction of all centers of curvature of these curves, i.e. the construction of the evolute of a curve. Our aim is to investigate the synthetic constructions without the use of coordinates and formulate the proofs of them. We newly model selected types of curves in GeoGebra dynamic system which is an additional output to our theoretical conclusions and also a significant teaching aid at the same time. The con- structions are meant to be dynamic and the curves are formed gradually as the traces of points or curves. All examples presented in this article are intended to be used in the undergraduate courses on kinematic geometry (mandatory courses for pre-service mathematics teachers who study teaching mathematics and descriptive geometry, i.e. the prospective secondary school teachers). The synthetic constructions together with their proofs demonstrated in GeoGebra dynamic system bring a new light into this area. It allows students to imagine the main idea of the proofs of the constructions and to investigate the properties of the curves more easily based on the pure geometry and visual aspects. Dynamic constructions, i.e. the possibility of changing positions of points and curves play the significant role here. GeoGebra offers also algebraic expressions which represent another tool for students how they can study and manip- ulate with those curves.

Název v anglickém jazyce

Construction and exploration of particular curves and evolutes of theirs using GeoGebra dynamic software

Popis výsledku anglicky

The article deals with the synthetic construction of specific planar curves which are defined by geometric motions and with the modeling of these constructions in GeoGebra dynamic system. We focus on the constructions of trajectories, envelopes, and centers of curvature and osculating circles of specific curves. We present a par- ticular construction of all centers of curvature of these curves, i.e. the construction of the evolute of a curve. Our aim is to investigate the synthetic constructions without the use of coordinates and formulate the proofs of them. We newly model selected types of curves in GeoGebra dynamic system which is an additional output to our theoretical conclusions and also a significant teaching aid at the same time. The con- structions are meant to be dynamic and the curves are formed gradually as the traces of points or curves. All examples presented in this article are intended to be used in the undergraduate courses on kinematic geometry (mandatory courses for pre-service mathematics teachers who study teaching mathematics and descriptive geometry, i.e. the prospective secondary school teachers). The synthetic constructions together with their proofs demonstrated in GeoGebra dynamic system bring a new light into this area. It allows students to imagine the main idea of the proofs of the constructions and to investigate the properties of the curves more easily based on the pure geometry and visual aspects. Dynamic constructions, i.e. the possibility of changing positions of points and curves play the significant role here. GeoGebra offers also algebraic expressions which represent another tool for students how they can study and manip- ulate with those curves.

Druh

D - Stať ve sborníku

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

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název statě ve sborníku

Electronic Proceedings of the 26th Asian Technology Conference in Mathematics

ISBN

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ISSN

1940-4204

e-ISSN

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Počet stran výsledku

11

Strana od-do

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Název nakladatele

Mathematics and Technology, LLC

Místo vydání

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Místo konání akce

Radford, Virginia, USA

Datum konání akce

13. 12. 2021

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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