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Um problema de optimização: de Euclides à actualidade
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Abstract(s)
Nesta comunicação apresentamos parte de uma investigação histórica acerca dos problemas de optimização. Nela, começámos por identificar os matemáticos que os
abordaram dando ênfase à forma como era elaborada a respectiva resolução, antes e depois de surgir a derivada. Tentamos também caracterizar os vários tipos de problemas que se podem encontrar. Depois analisámos os programas oficiais portugueses e os manuais escolares com o objectivo de verificar os que abordavam os problemas de optimização, que problemas abordam e a forma como estes eram resolvidos.
A primeira referência que encontramos foi na obra Elementos de Euclides no século IV. a. C., ou seja, antes de se usar a derivada. Assim, nesta comunicação iremos indicar os
problemas de optimização presentes na obra de Euclides. Em particular será analisada a resolução de um desses problemas e estabelecer o paralelo com a resolução, de um problema idêntico, que hoje se apresenta nos manuais escolares, sem o recurso à derivada.
In this paper we present a part of an historic research about optimization problems. We start identifying the mathematicians witch have studied them centring in the way they solve them, before and after the appearance of the derivative. We also tried to identify the different kinds of problems that we can find. Next, we analysed the Portuguese official programs and the textbooks with the aim of identifying which of them included optimization problems, which are these problems and how they are solved. The first problems we have found were in the book “The thirteen books of Euclid’s Elements” from Euclid in IV b. C, before the use of the derivative. So, in this paper we are going to show the optimization problems found in these books and the way he proofs them. Then we will also make a parallelism with the solution we found in an actual textbook.
In this paper we present a part of an historic research about optimization problems. We start identifying the mathematicians witch have studied them centring in the way they solve them, before and after the appearance of the derivative. We also tried to identify the different kinds of problems that we can find. Next, we analysed the Portuguese official programs and the textbooks with the aim of identifying which of them included optimization problems, which are these problems and how they are solved. The first problems we have found were in the book “The thirteen books of Euclid’s Elements” from Euclid in IV b. C, before the use of the derivative. So, in this paper we are going to show the optimization problems found in these books and the way he proofs them. Then we will also make a parallelism with the solution we found in an actual textbook.
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Citation
Esteves, A.E.; González, M. T. (2009). Um problema de optimização: de Euclides à actualidade. En M.J. González; M. T. González; J. Murillo (eds) Investigación en Educación Matemática. Comunicaciones de los grupos de investigación. XIII Simposio de la SEIEM. Santander