História da matemátização da braquistócrona e abordagens didáticas.

Abstract

In the work, we deal with the studies of a problem launched in the 17th century Johann Bernoulli to all renowned mathematicians in that period, which he named Brachistochronous, this problem consists in discovering which curve corresponds to the fastest descente of a given particle, which by the action of gravity will move from a higher point to a lower point in the shortest possible time, in the first publication out of its own solution the answer elaborated by Leibniz was presented, after the republiction two others appeared, the authors being Jakob Bernoulli,Isaac Newton, all the answers refer to the cycloid curve as an answer, and they were obtained through random paths. The historical context of Brachistochronous includes the Discovery of several interesting properties, which were fundamental for the implementation of optimizations for the use of Society such as the onstruction of roller coasters or even the construction of half piper skate rinks. Then, knowing the efficiency of the use of manipulable concrete material in the teaching and learning process, which enables us to easily understand abstract mathematical concepts, we designed a model to remove doubts about the solution of the problem. In addition, we interact with Brachistochronous problem with technological tools, using the free software instituted as Geogebra we trace step by step how to build such curves and conclude that the cycloid is the solution.