文档介绍：摘要
极坐标法是一种重要的解题方法,虽然高中数学教材已经删去极坐标的内容,但这一思想和方法对解决平面几何问题和高等数学问题都有很重要的作用,有必要加以深入研究。
本文首先对极坐标的基础知识进行阐述,给出了极坐标的相关概念,以及求曲线方程的方法与步骤,并求出了三种圆锥曲线统一的极坐标方程,然后讨论了极坐标在平面解析几何中的应用,最后探讨了极坐标在解决高等数学问题的应用。通过对极坐标在数学各方面的应用的探讨,我们能够发现极坐标有很大的优越性。通过探讨研究,使我们对极坐标这一思想和方法有更深的了解,并使学生对高中平面解析几何内容有完整的把握,有更深层次的掌握。同时,这种对知识的深入掌握可以使教育者更好的完成对其的教学任务。
关键词:极坐标;应用;优越性
Abstract
The method of using the polar coordinates is an usually used method. Although the content of the method has been deleted in the process of editing the mathematical textbook for middle school students, this method is very important to solve the problem of plane geometry and advanced mathematics. It is necessary to study this method further.
First this paper illustrates the basic knowledge of polar coordinates. The writer gives the relative concepts of polar coordinates and the method and steps of solving curve equation, and work out the polar coordinates equation of three taper curves. Second it discusses the application of the method in plane analytic geometry. And then it probes into the application of the method in solving the advanced mathematical problem. By exploring the application of polar coordinates in many mathematical aspects, we may notice the advantages of polar coordinates and its certain applicable range. By studying, it makes us understand the concepts and the thinking further. It also makes the students grasp the content of plane analytic geometry wholly and deeper in middle school. Also, the deep understanding of the knowledge makes the teacher finish the educational tasks better.
Keywords: polar coordinates; application; advantages
前言
第一个用极坐标来确定平面上点的位置的是牛顿。他的《流数法与无穷级数》,大约于1671年写成,出版于1736年。此书包括解析几何的许多应用,例如按方程描出曲线,书中创见之一,是引进新的坐标系。《教师学报》上发表了一篇基本上是关于极坐标的文章,。,而且自由地应用极坐标去研究曲线。
在平面内建立直角坐标系,是人们公认的最容易接受并且被经常采用的方法,但它并不是确定点的位置的唯一方法。有些复杂的曲线用直角坐标表示,形式极其复杂,但用极坐标表示,就变得十分简单且便于处理,在此基础上解决平面解析几何问题也变的极其简单。通过探究极坐标在平面解析几何中的广泛应用,使我们能够清楚的认识到,用极坐标来解决某些平面解析几何问题和