论文标题
笛卡尔片段中功能概念的介绍
An introduction to the concept of function within Descartes's algebra of segments
论文作者
论文摘要
在他的géométrie（1637年）中，笛卡尔介绍了段的代数。这是在创建差分微积分之前对可变数量的数学处理的基本步骤。它是一个带有符号的代数，但没有数字，其中几何变量之间的协方差（受统治者和指南针构造或其他几何结构都可以用符号方程表示）。通过使用代数操作，可以轻松推断相应的几何构建体的性质，包括产生有理函数图的构造。我们认为，通过笛卡尔代数对功能的研究可以是有效的，可以在中学中教学和学习功能概念。首先，它避免了对实数的引用；其次，将公式的解释为几何结构，反之亦然，促进了从被理解为过程到被理解为对象的函数的函数的“过渡”。
In his Géométrie (1637) Descartes introduces the algebra of segments. This is a fundamental step in the mathematical treatment of variable quantities before the creation of differential calculus. It is an algebra with symbols but without numbers, in which the covariation between geometric variables, constrained by ruler and compass constructions or with other geometric constructions, can be expressed with symbolic equations. By using algebraic manipulations, it is possible to easily deduce the properties of the corresponding geometric constructions, including those that produce graphs of rational functions. We believe that the study of functions through Descartes's algebra can be didactically effective in teaching and learning the concept of function in secondary school. Firstly, it avoids the reference to real numbers; secondly, the interpretation of formulas as geometric constructions and vice versa facilitates the "transition" from functions understood as processes to functions understood as objects.
