From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes

Ezequias Adolfo Domingas Cassela; Amado Leonardo André

doi:doi:10.11648/j.pamj.20211004.11

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From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes

Ezequias Adolfo Domingas Cassela, Amado Leonardo André

Published in Pure and Applied Mathematics Journal (Volume 10, Issue 4)

Received: 19 July 2021 Accepted: 28 July 2021 Published: 4 August 2021

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Abstract

This article aims to study the ellipse from the perspective of pure or synthetic geometry to the representation of points on a plane through the use of real numbers, as well as the representation and classification of this conic curve through the use of equations. The perspective developed in this article is based on the view of René Descartes, in considering that “the algebraic steps in a demonstration should really correspond to a geometric representation.” The relevance of this article is to bring a reflection that eliminates the study of Analytical Geometry through ready-made and finished formulas, without satisfactory justification and without a logical chain that gives a greater meaning to the studied concepts. In general, the study developed in this article emphasizes the demonstration of results based on propositions adapted a priori, whose ability to be developed is aimed at establishing an "if...then" type of reasoning, making conjectures involving various knowledge already acquired and confirming such truths from a logical system, using definitions and propositions. Therefore, the demonstrations made in the scope of Synthetic Geometry will help to establish a connection with the equations obtained from the perspective of Analytical Geometry, serving as a consultation for students and professors of Analytical Geometry, thus avoiding sudden transitions between contents of degrees of distinct difficulties.

Published in	Pure and Applied Mathematics Journal (Volume 10, Issue 4)
DOI	10.11648/j.pamj.20211004.11
Page(s)	89-95
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Pure Geometry, Algebraic Thought, Conic Curves, Study of the Ellipse

References

[1]	Cassela, EAD. (2020). Da Matemática nativa presente no pensamento das autoridades tradicionais da tribu Umbundu com respeito a forma do ondjango no Cuito/Bié-Angola para problemas isoperimétricos da Geometria Plana. European Reviw of Artistic Studies, v. 11, n. 2, p. 69-80.
[2]	Rich, B. (1972). Geometria Plana. Coleção Schaum. Brasil: Eitora Mc Graw-Hill, Ltda, p. 1.
[3]	Klein, F. (1948). Elementary Mathematics from an Advanced Standpoint. Geometry, New York. Dover.
[4]	Pickover, CA. (2009). O livro da Matemática. New York: NY 10016, VS, p. 136.
[5]	Guimarães, RMS. (2014). Geometria Analítica no plano. Pensar e ensinar Geometria. Master’s Thesis, Universidade da Beira Interior, Covilhã, Portugal, p. 3.
[6]	Cassela, EAD., & DE Nascimento, RM., (2020). Estudo da Circunferência à luz dos princípios axiomáticos de René Descartes. Um olhar ao context de Ensino-Aprendizagem da Escola Superior Pedagógica do Bié. Revemat, v. 15, p. 1-21.
[7]	Boyer, CB (2003). História da Matemática. Edgard Blucher, São Paulo.
[8]	Guimarães, CS. (2008). Matemática em nível Ime Ita. São José dos Campos. Vestseller, p. 11.
[9]	Monteiro, RM. (2014). Resgate do teorema de Dandelin no estudo de cónicas com o Geogebra. Master’s Thesis, Universidade Federal do Espítrito Santo, Brasil. Disponível em: http://repositório.ues.br/handle/10/4819.
[10]	Fuller. G., Connors, J., & Levy, J. (2020). COVID-19 and its implications for thrombosis and anticoagulation. Blood, 135, 2033 - 2040.
[11]	Cassela. EAD (2018). Estudo da Geometria Analítica no Contexto cultural do Cuito. Master’s Thesis, Universidade da Beira Interior Portugal.
[12]	Cassela. EAD (2019). Abordagem sintética e analítica das cónicas. Uma perspectiva de Ensino em contexto. Editora Templários, Lisboa, Portugal.
[13]	Santos, EC. & Cassela, EAD. (2021). Interface entre a elipse e a circunferência: Contributo da etnomodelagem no ensino da Geometria Analítica por meio de cestaria. Matemática & Ciência, v. 4, n. 1, p. 73-86.
[14]	Alcopyan, A. V., Zaslavsky A. A (2007). Geometry of conics. American Matematical Society.
[15]	Queiró, F., J., A elipse, a parábola e hipérbole - propriedades e aplicações (2010). Master’s Thesis, Universidade Federal de Santa Catarina, Brasil.

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Ezequias Adolfo Domingas Cassela, Amado Leonardo André. (2021). From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes. Pure and Applied Mathematics Journal, 10(4), 89-95. https://doi.org/10.11648/j.pamj.20211004.11

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ACS Style

Ezequias Adolfo Domingas Cassela; Amado Leonardo André. From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes. Pure Appl. Math. J. 2021, 10(4), 89-95. doi: 10.11648/j.pamj.20211004.11

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AMA Style

Ezequias Adolfo Domingas Cassela, Amado Leonardo André. From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes. Pure Appl Math J. 2021;10(4):89-95. doi: 10.11648/j.pamj.20211004.11

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@article{10.11648/j.pamj.20211004.11,
  author = {Ezequias Adolfo Domingas Cassela and Amado Leonardo André},
  title = {From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes},
  journal = {Pure and Applied Mathematics Journal},
  volume = {10},
  number = {4},
  pages = {89-95},
  doi = {10.11648/j.pamj.20211004.11},
  url = {https://doi.org/10.11648/j.pamj.20211004.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20211004.11},
  abstract = {This article aims to study the ellipse from the perspective of pure or synthetic geometry to the representation of points on a plane through the use of real numbers, as well as the representation and classification of this conic curve through the use of equations. The perspective developed in this article is based on the view of René Descartes, in considering that “the algebraic steps in a demonstration should really correspond to a geometric representation.” The relevance of this article is to bring a reflection that eliminates the study of Analytical Geometry through ready-made and finished formulas, without satisfactory justification and without a logical chain that gives a greater meaning to the studied concepts. In general, the study developed in this article emphasizes the demonstration of results based on propositions adapted a priori, whose ability to be developed is aimed at establishing an "if...then" type of reasoning, making conjectures involving various knowledge already acquired and confirming such truths from a logical system, using definitions and propositions. Therefore, the demonstrations made in the scope of Synthetic Geometry will help to establish a connection with the equations obtained from the perspective of Analytical Geometry, serving as a consultation for students and professors of Analytical Geometry, thus avoiding sudden transitions between contents of degrees of distinct difficulties.},
 year = {2021}
}

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T1  - From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes
AU  - Ezequias Adolfo Domingas Cassela
AU  - Amado Leonardo André
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DO  - 10.11648/j.pamj.20211004.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
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PB  - Science Publishing Group
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AB  - This article aims to study the ellipse from the perspective of pure or synthetic geometry to the representation of points on a plane through the use of real numbers, as well as the representation and classification of this conic curve through the use of equations. The perspective developed in this article is based on the view of René Descartes, in considering that “the algebraic steps in a demonstration should really correspond to a geometric representation.” The relevance of this article is to bring a reflection that eliminates the study of Analytical Geometry through ready-made and finished formulas, without satisfactory justification and without a logical chain that gives a greater meaning to the studied concepts. In general, the study developed in this article emphasizes the demonstration of results based on propositions adapted a priori, whose ability to be developed is aimed at establishing an "if...then" type of reasoning, making conjectures involving various knowledge already acquired and confirming such truths from a logical system, using definitions and propositions. Therefore, the demonstrations made in the scope of Synthetic Geometry will help to establish a connection with the equations obtained from the perspective of Analytical Geometry, serving as a consultation for students and professors of Analytical Geometry, thus avoiding sudden transitions between contents of degrees of distinct difficulties.
VL  - 10
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Author Information

Ezequias Adolfo Domingas Cassela

Department of Exact Sciences, Bié Higher Pedagogical School, Cuito/Bié, Angola
Amado Leonardo André

Department of Exact Sciences, Bié Higher Pedagogical School, Cuito/Bié, Angola

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Plain Text BibTeX RIS

APA Style

Ezequias Adolfo Domingas Cassela, Amado Leonardo André. (2021). From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes. Pure and Applied Mathematics Journal, 10(4), 89-95. https://doi.org/10.11648/j.pamj.20211004.11

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ACS Style

Ezequias Adolfo Domingas Cassela; Amado Leonardo André. From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes. Pure Appl. Math. J. 2021, 10(4), 89-95. doi: 10.11648/j.pamj.20211004.11

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AMA Style

Ezequias Adolfo Domingas Cassela, Amado Leonardo André. From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes. Pure Appl Math J. 2021;10(4):89-95. doi: 10.11648/j.pamj.20211004.11

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@article{10.11648/j.pamj.20211004.11,
  author = {Ezequias Adolfo Domingas Cassela and Amado Leonardo André},
  title = {From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes},
  journal = {Pure and Applied Mathematics Journal},
  volume = {10},
  number = {4},
  pages = {89-95},
  doi = {10.11648/j.pamj.20211004.11},
  url = {https://doi.org/10.11648/j.pamj.20211004.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20211004.11},
  abstract = {This article aims to study the ellipse from the perspective of pure or synthetic geometry to the representation of points on a plane through the use of real numbers, as well as the representation and classification of this conic curve through the use of equations. The perspective developed in this article is based on the view of René Descartes, in considering that “the algebraic steps in a demonstration should really correspond to a geometric representation.” The relevance of this article is to bring a reflection that eliminates the study of Analytical Geometry through ready-made and finished formulas, without satisfactory justification and without a logical chain that gives a greater meaning to the studied concepts. In general, the study developed in this article emphasizes the demonstration of results based on propositions adapted a priori, whose ability to be developed is aimed at establishing an "if...then" type of reasoning, making conjectures involving various knowledge already acquired and confirming such truths from a logical system, using definitions and propositions. Therefore, the demonstrations made in the scope of Synthetic Geometry will help to establish a connection with the equations obtained from the perspective of Analytical Geometry, serving as a consultation for students and professors of Analytical Geometry, thus avoiding sudden transitions between contents of degrees of distinct difficulties.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes
AU  - Ezequias Adolfo Domingas Cassela
AU  - Amado Leonardo André
Y1  - 2021/08/04
PY  - 2021
N1  - https://doi.org/10.11648/j.pamj.20211004.11
DO  - 10.11648/j.pamj.20211004.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 89
EP  - 95
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20211004.11
AB  - This article aims to study the ellipse from the perspective of pure or synthetic geometry to the representation of points on a plane through the use of real numbers, as well as the representation and classification of this conic curve through the use of equations. The perspective developed in this article is based on the view of René Descartes, in considering that “the algebraic steps in a demonstration should really correspond to a geometric representation.” The relevance of this article is to bring a reflection that eliminates the study of Analytical Geometry through ready-made and finished formulas, without satisfactory justification and without a logical chain that gives a greater meaning to the studied concepts. In general, the study developed in this article emphasizes the demonstration of results based on propositions adapted a priori, whose ability to be developed is aimed at establishing an "if...then" type of reasoning, making conjectures involving various knowledge already acquired and confirming such truths from a logical system, using definitions and propositions. Therefore, the demonstrations made in the scope of Synthetic Geometry will help to establish a connection with the equations obtained from the perspective of Analytical Geometry, serving as a consultation for students and professors of Analytical Geometry, thus avoiding sudden transitions between contents of degrees of distinct difficulties.
VL  - 10
IS  - 4
ER  -

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