| 对合的二重元素在解析几何画图中的一个应用——抛物线上的点的一种几何画法 |
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| 引用本文： | 马立. 对合的二重元素在解析几何画图中的一个应用——抛物线上的点的一种几何画法[J]. 曲靖师范学院学报, 1988, 0(3) |
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| 作者姓名： | 马立 |
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| 作者单位： | 曲靖师专数学系 |
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| 摘 要： | 解析几何中,椭圆、双曲线、抛物线都可以依据方程式用描点法作图。此外,椭圆和双曲线还可以利用参数方程x=acosθy=bsinθ和x=ascθy=btgθ用初等几何方法作出其上的一些点。而抛物线的类似作图在一般解析几何书中则没有提及。本文由对合对应二重点的作法及性质得到启示,给出了一种只需知道焦点和准线,不需经由方程和计算,而是从定义出发纯几何地画出抛物线上的点的一种方法。
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| 关 键 词： | 对合对应 二重元素 抛物线 |
The Application of Invontory Bipoints Element Iu The Cntustructino of Analytic Geometry |
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| Ma Li. The Application of Invontory Bipoints Element Iu The Cntustructino of Analytic Geometry[J]. Journal of Qujing Normal College, 1988, 0(3) |
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| Authors: | Ma Li |
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| Affiliation: | Depar tmene of maths |
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| Abstract: | In analytic geomtery, ellipse, hyperbola and parabola can be construoted by using the tracing point method according to the equation. Besidessome points on the ellipse and hyperbola can also be constructed by using the elementary geometry according to theparametric equationThe analogous construction of parabola has not been mentioned in ordinary analytic geometry books. The article gets some enlightment from the construction and property of involutory correspondence bipoints. And therefore obtains a method of constructing the points on the parabola by means of pure geometry according to the definltion. The method needs only focus and directrjx, not equatjon or calculatjon. |
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| Keywords: | invlutory correspondence double parabola. |
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