| 三类叶形线的性质 |
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| 引用本文： | 石勇国,何光,朱凯.三类叶形线的性质[J].内江师范学院学报,2008,23(8):25-27. |
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| 作者姓名： | 石勇国 何光 朱凯 |
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| 作者单位： | 内江师范学院数学与信息科学学院//四川省高等学校数值仿真重点实验室,四川,内江,641112 |
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| 基金项目： | 四川省教育厅资助项目，内江师范学院大学生科研课题 |
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| 摘 要： | 引入了曲线周期、函数周期以及叶形线的概念，给出了曲线对称性的判定条件，分别构造了谐波叶形线，齿轮叶形线和齿纹叶形线，分别给出了它们的函数表达式、函数周期、曲线周期、极点处的切线以及参数与叶数、叶形之间的关系．得到任意叶数和多种形状叶形线的极坐标方程，推广了玫瑰线．
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| 关 键 词： | 平面曲线 玫瑰线 叶形线 |
Properties of the Three Classes of Foliam Curves |
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| SHI Yong-guo,HE Guang,ZHU Kai.Properties of the Three Classes of Foliam Curves[J].Journal of Neijiang Teachers College,2008,23(8):25-27. |
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| Authors: | SHI Yong-guo HE Guang ZHU Kai |
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| Institution: | (College of Mathematics and Information Science//Key Laboratory of Numerical Simulation of Sichuan Province, Neijing Normal University, Neijiang, Sichuan 641112, China) |
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| Abstract: | The definitions of curvilinear period,functional period and folium curve are introduced.The sufficient conditions for symmetrical curve are also presented.The harmonic folium curve,gear folium curve and tooth profile folium curve are constructed and their mathematical expressions,functional periods,curvilinear periods,the tangent at the pole and the relationships between the number(shape) of leaf and the parameters are respectively given.The polar equations of folium curve with an arbitrary number of leaves or various kinds of shapes are obtained.Thus the rose is generalized. |
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| Keywords: | plane curve rose folium curve |
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