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解析几何其本质是用代数的方法研究几何图形的性质,即通过引进直角坐标系,建立点与坐标、曲线和方程的对应关系,将几何问题转化为代数问题,从而用代数方法研究几何问题。解析几何充分体现了数形结合的数学思想,是教学中渗透数形结合思想的有效载体。有了这个强有力的工具,我们就可以通过建立曲线的方程来研究曲线的几何性质。南开大学的顾沛教授在讲授《数学文化》中指出:从变化的数学模型中研究不变的性质是数学研究的方向之一。这个观点
The essence of analytic geometry is to study the properties of geometry by algebraic method. That is to say, geometric problems are transformed into algebraic problems through the introduction of rectangular coordinate system, the corresponding relations between points, coordinates, curves and equations. Analytical geometry fully embodies the mathematics thought of combining figures with form, which is an effective carrier for penetrating the idea of combining figures with form in teaching. With this powerful tool, we can study the geometric properties of the curve by establishing the equation of the curve. Professor Gu Pei of Nankai University pointed out in his article “Mathematical Culture” that it is one of the directions of mathematical research to study the invariant nature from the changing mathematical model. This view