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By using our site, you agree to our collection of information through the use of cookies. To learn more, view our Privacy Policy. To browse Academia. Aldous Schafer. Marcio Vieira. The objective of this study is to investigate how students presented the two different environments - from one side paper and pencils and other information, include notions of straight lines and circumferences, and the formalization of their equations in Cartesian, polar and parametric representation.
In this sense we analyze the expected institutional relations and existing for the study of these planar curves in Analytic Geometry in secondary and higher education. We seek to identify the retrospective knowledge of students and see how the timing of representations, through work with the views parametric, cartesian and polar, favors the identification of plane curves through the graphics ostentatious.
In this diapason, we note the possibility of implementation this articulation of the three views of these planar curves in both school steps. For the development of this research, we began to preliminary studies related to the topic discussed, which guided us toward topics and problems related to the cartesian representation, parametric and polar flat curves present in articles, dissertations and national and international theses of the last 10 ten years, magazines and institutions, with access via libraries and Internet.
Then we present some similar research dealing with the transition between secondary and higher education. Elected as a central theoretical framework to approach the Anthropological Theory of the Didactic - TAD , particularly in praxeology notions - overt and not ostentatious - and as support, we consider the theoretical approaches to the notion of point of view, as Dias and Rogalski; the notion of Douady framework; the notion of knowledge levels expected of students, according to Robert and the computer transposition notion Balacheff.
Being a qualitative study, we present the analysis as instruments of institutional documents and textbooks, the development of a teaching sequence, and the trial and preliminary analysis, a priori, a posteriori and its validation. In this teaching sequence, we propose didactic sessions that take the student to make a link between the points of view cartesian, polar and parametric and the formalization of lines and circles equations, in the plane, favoring the understanding of these mathematical objects.
Such a possibility would be guided based on i the mathematical landscape of Analytical Geometry, especially lines and circles, in the plan; Ii the expected institutional relationships and existing on these curves in secondary and higher education and iii the use of free graphics plotters as Winplot and GeoGebra. For the analysis of textbooks and teaching sequence used by the elaborate Days analysis grid, which was instrumental in identifying both existing mathematical and educational organizations, as expectations in terms of retrospective knowledge expected of students in the transition from education secondary and higher education for the study of these objects.
In the subsequent analysis it was found that the relationship between the cartesian representations, parametric and polar plane curves, with mediation and interaction of two rooms, a paper and pencil and other information, to promote student understanding of line and circumference of the notions study of analytic geometry flat.
For future research study indicated the coordinates and vectors in space already in high school, which would favor the study of line and circle in space and their cartesian, parametric and polar representations in the transition from secondary and higher education.
Pedro Guilherme. Mauricio Seijas. Isaque Sousa. E Adelio Ferraz de Castro. Ulisses Pereira. Willian Erthal. Carolina Quinelato. Breno Coutinho. Jeremias Alfredo Sousa. Guilherme Medeiros. Lorimi Hoel'tuzam. Alex Sandro Rodrigues Silva. Lucas Lopes. Pedro Crespo. Geane Niemeyer. Anderson Carlos. Ran Ezequias Cassela , Carlos Margarido. Melquesedeque Cardoso Borrete. Carla Andrucioli Carnesecca. Log in with Facebook Log in with Google.
Remember me on this computer. Enter the email address you signed up with and we'll email you a reset link. Need an account? Click here to sign up. Download Free PDF. Lourdinha Machado. Related Papers. Conicas e quadricas Jacir Venturi.
Algebra Linear e Geometria Analitica. ISBN 1. Aos milhares de ex-alunos, com os quais muito aprendi. Aos colegas pelo incentivo. E, por fim, dois agradecimentos muito especiais.
E, para tanto, como este livro foi pensado? E, no caso de ainda sobrar tempo, recomenda-se 1. Da mesma forma, cada professor tem suas peculiaridades ainda bem! A Figura 1. Na Figura 1. Esta grandeza velocidade seria representada por um segmento orientado uma seta - Figura 1. Na A Figura 1. Figura 1. A Figura l. Considera-se o vetor zero ortogonal a qualquer vetor. NB I H Figura 1. Tomemos um ponto A qualquer Figura 1. QJ Figura 1. Com base na Figura 1.
QJ s A Figura 1. Por exemplo, na Figura 1. Logo, V V Exemplos 1. DC Figura 1. Embora estejamos simbolizando a base como um conjunto, a pensamos como um conjunto ordenado. Trata-se da base que determina o conhecido sistema cartesiano ortogonal xOy. Dado um vetor v qualquer do plano Figura 1. As Figuras l. Vetor definido por dois pontos Consideremos o vetor AB de origem no ponto A x 1 ,y1 e extremidade em B x2 ,y2 Figura 1.
JI QJ 4 Figura 1. Jl3 u. Determinar, no eixo Ox, um ponto P que seja equidistante dos pontos A -1, -2 eB 5, JS' 5 5. X Figura 1. As Figuras 1. M Figura 1. Problemas propostos 1. Sejam os pontos A -5, 1 e B l, 3. Representar graficamente esse segmento. O'Q 1 o Sendo A - 2, 1, 3 e B 6, - 7, 1 extremidades de um segmento, determinar: -o VI Determinar o ponto D.
Obter um ponto P do eixo das abscissas equidistante dos pontos A 3, -1, 4 e B l, -2, J3 VI J3 2 C 6,-l,3 eD l,-9,7 3 ro. P 3,0,0 Na Figura 2. Figura 2. Logo, A Figura 2. Logo, 3 '1.
Vetores E Geometria Analitica - Paulo [34mz3ken6].Uploaded by
Problemas propostos 1. Sejam os pontos A -5, 1 e B l, 3. Representar graficamente esse segmento. O'Q 1 o Sendo A - 2, 1, 3 e B 6, - 7, 1 extremidades de um segmento, determinar: -o VI Determinar o ponto D. Obter um ponto P do eixo das abscissas equidistante dos pontos A 3, -1, 4 e B l, -2, J3 VI J3 2 C 6,-l,3 eD l,-9,7 3 ro. P 3,0,0 Na Figura 2. Figura 2. Logo, A Figura 2. Logo, 3 '1. Determinar a. A Figura 2. O'Q '1 o Seja o cubo de aresta a representado na Figura 2. QJ ::l QJ J2,1,-1 Figura 3.
A Figura 3. Assim, nesse dispositivo temos imediata- Figura 3. Calcular jABxACj. A B Logo, de acordo com o problema an- Figura 3. Considerando a Figura 3.
Obter um vetor ortogonal ao plano determinado pelos pontos A 2, 3, 1 , B l, -1, 1 e C 4, 1, Com base na Figura 3. J74 J35 C O, l,O ou C 0,-,0 2 Figura 4. I ' ''' e w Figura 4.
Sendo vxw um vetor orto- ' Portanto, ,, ,,. QJ 2 s QJ J3 Figura 5. Se desejarmos obter pontos de r, basta atribuir valores para t. Se t assumir todos os valores reais, teremos todos os infinitos pontos da reta. A Figura 5. O'Q '1 o As Figuras 5. Na Figura 5. I Figura 5. I I I Figura 5. Com base na Figura 5. Apenas Pi e -o Figura 6.
X Figura 6. Portanto, trata-se de um plano paralelo a xOy e que intercepta o eixo Oz perpendicularmente em O, O, 6. Pela e -o Figura 6. QJ Por exemplo, determinar o ponto A E r que tem abscissa zero. Logo, A 0,- 1,4. Determinar o valor de a para que os pontos A a, 1, 9 , B 2, 3, 4 , C - 4, - 1, 6 e -o D O, 2, 4 sejam coplanares.
Dados a retare o plano n, determinar o valor de m para que se tenha ri ln e r. Sejam a reta r e o plano n dado por O plano que intercepta os eixos coordenados nos pontos de abscissa, ordenada e -a - QJ cota iguais a - 3, 6 e - 5, respectivamente.
O plano paralelo ao eixo z que intercepta o eixo x em - 3 e o y em 4. Existem infinitos. JS 3 7t 3 b d are cos r 6 -vl4 C 12 li. Figura 7. A Figura 7. Audio Software icon An illustration of a 3. Software Images icon An illustration of two photographs. Images Donate icon An illustration of a heart shape Donate Ellipses icon An illustration of text ellipses.
Metropolitan Museum Cleveland Museum of Art. Internet Arcade Console Living Room. Books to Borrow Open Library. Search the Wayback Machine Search icon An illustration of a magnifying glass. To browse Academia. Rafael Oliveira. Andrey Freitas. Rafael Paes. Fabiana Nascimento. Ligia Lara. Ana Carolina Borges. Mauricio Seijas. E Adelio Ferraz de Castro.
Ulisses Pereira. Francisco Sousa. Willian Erthal. Samela Barbosa. Danda Oliveira. Nathan Mota. Marcelo Wanderley de Almeida. Jeremias Alfredo Sousa. Guilherme Medeiros. Lorimi Hoel'tuzam.
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