Disertación de Maestría
DOI
https://doi.org/10.11606/D.55.2020.tde-06082020-104936
Documento
Autor
Nombre completo
Daiane Antônia de Menezes Lima
Dirección Electrónica
Área de Conocimiento
Fecha de Defensa
Publicación
São Carlos, 2020
Director
Tribunal
Artioli, Vanessa Rolnik (Presidente)
Gonçalves, Alexandre Casassola
Menin, Olavo Henrique
Título en portugués
Atividades sobre problemas inversos em pré-cálculo
Palabras clave en portugués
Geometria analítica
Problema inverso
Semelhança de triângulos
Técnicas de resolução de problemas
Trigonometria
Resumen en portugués
Título en inglés
Activities on inverse problems in pre-calculus
Palabras clave en inglés
Analytical geometry
Inverse problem
Problem solving techniques
Similarity of triangles
Trigonometry
Resumen en inglés
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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Fecha de Publicación
2020-08-06