A matemática e a história dos números decimais

Abstract

This work has as its object of study of the representation decimal fractions developed by Simon Stevin, in his work De Thiende in 1585. This new representation of decimal fractions lead to the decimal numbers that we know on present days, in other words, numbers that we use comma to separate the integer part of the decimal part. Simon Stevin described (in De Thiende) the way to solve any arithmetic with the use of decimal numbers. We studied about the resolution of the fundamental operations of arithmetic (addition, subtraction, multiplication and division) and the calculation of roots (square, cubic, and others) by means of algorithms to illustrate the efficiency and inefficiency in the use of the algorithm that refers to the mathematics learning. We discuss also two types of thought, the instrumental thought and theoretical thought, exemplifying the differences and complementarity between them showing the importance for the development of mathematical learning. The binding of two different periods, that are the XVI century and the XX century, with respect to computing, when Simon Stevin brought a representation, in other words, the decimal numbers aiming to facilitate the calculations in the XVI century, and century XX, the creation of the computer enabled these calculations become even simpler. But this creation was only possible from the time that there was an organization of numbers in digit, made by Simon Stevin in the late XVI century. The organization of numerical sets by creating new ones in order to supply the needs of humans and their evolutions, thereby showing that the representation of Simon Stevin followed this evolution. Epistemology and history of decinals numbers allowed that knowledge about this would be better understood in the context of mathematics education.