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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2020.tde-06082020-104936
Document
Author
Full name
Daiane Antônia de Menezes Lima
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2020
Supervisor
Committee
Artioli, Vanessa Rolnik (President)
Gadotti, Marta Cilene
Gonçalves, Alexandre Casassola
Menin, Olavo Henrique
Title in Portuguese
Atividades sobre problemas inversos em pré-cálculo
Keywords in Portuguese
Geometria analítica
Problema inverso
Semelhança de triângulos
Técnicas de resolução de problemas
Trigonometria
Abstract in Portuguese
Este trabalho consiste de um estudo sobre problemas inversos voltados para alunos e professores do Ensino Médio. Discutimos definições, problemas reais da antiguidade que hoje em dia são classificados como inverso e problemas da atualidade que têm alavancado o desenvolvimento de técnicas de diagnóstico e previsões no campo da saúde, da indústria e da defesa, bem como em diversas outras áreas. Em particular, estudamos detalhadamente quatro casos: o problema inverso de determinar a altura do furo de um reservatório, o problema inverso de determinar o ângulo de inclinação no lançamento de um projétil, o problema inverso de determinar a massa e a localização de uma pepita de ouro no fundo do rio e problemas inversos nas jogadas de tabela em um jogo de sinuca. O projeto foi fundamentalmente baseado na referência GROETSCH, C. W., Inverse problems: activities for undergraduates, Whashington: the mathematical association of America, 1999. Para complementar, utilizamos livros de Matemática e Física básicas, artigos de jornais e pesquisa na internet. Para nos auxiliar nas interpretações dos casos e ilustrar o texto, utilizamos o software GeoGebra. Finalmente, analisamos os resultados de cada caso separadamente e em seguida ressaltamos as diferenças entre os casos dentro de um contexto geral.
Title in English
Activities on inverse problems in pre-calculus
Keywords in English
Analytical geometry
Inverse problem
Problem solving techniques
Similarity of triangles
Trigonometry
Abstract in English
This work consists of a study on inverse problems aimed at high school students and teachers. We discuss definitions, real problems of antiquity that today are classified as inverse, and current problems that have leveraged the development of diagnostic and forecasting techniques in the field of health, industry and defense, as well as in several other areas. In particular, we study in detail four cases: the inverse problem of determining the height of a reservoirs hole, the inverse problem of determining the angle of inclination when launching a projectile, the inverse problem of determining the mass and location of a nugget of gold at the bottom of the river and inverse problems in table plays in a game of pool. The project was fundamentally based on the reference GROETSCH, C.W., Inverse problems: activities for undergraduates, Whashington: the mathematical association of America, 1999. In addition, we used basic mathematics and physics books, newspaper articles and internet research. To help us interpret the cases and illustrate the text, we use the GeoGebra software. Finally, we analyze the results of each case separately and then we highlight the differences between the cases within a general context.
 
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Publishing Date
2020-08-06
 
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