| 二次型化简二次曲线方法的探究 |
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| 引用本文： | 韩凌燕.二次型化简二次曲线方法的探究[J].山东科学,2008,21(2):52-54. |
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| 作者姓名： | 韩凌燕 |
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| 作者单位： | 西安建筑科技大学理学院,陕西西安,710055 |
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| 基金项目： | 陕两省教育厅专项科研基金
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西安建筑科技大学校科研和教改项目 |
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| 摘 要： | 通过结合解析几何与代数理论知识，利用化二次型为标准形的通常方法，给出了化简二次曲线的两种思路：合同变换和正交变换．前者是在不着重研究曲线几何性质时常用的一种方法，它的标准型不唯一，而后者相反．文中讨论了它们在实际例题中的应用．
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| 关 键 词： | 变换 移轴 转轴 不变量 |
Research on the Simplification of Second-order Curves to Normal Curves |
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| HAN Ling-yan.Research on the Simplification of Second-order Curves to Normal Curves[J].Shandong Science,2008,21(2):52-54. |
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| Authors: | HAN Ling-yan |
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| Institution: | HAN Ling-yan (School of Sciences, Xi＇ an University of Architecture and Technology, Xi＇ an 710055, China) |
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| Abstract: | We present two approaches to simplify second-order curves： the congruent and orthogonal transfonn, which are based on analytic geometry, algebra theory, and the ordinary approaches of the simplification of second-order curves to normal ones. The congruent transform is an approach that does not emphasize the geometric propeties of curves, and whose normal form is not unique. However, the orthogonal transform is an opposite approach. We also discuss their applications to practical instances. |
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| Keywords: | transform axis shift axis rotation invariant |
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