笛卡儿叶形线
![a=1](/Images/godic/202501/13/Kartesisches-Blatt.svg3137.png")
笛卡儿叶形线是一个代数曲线，首先由笛卡儿在1638年提出。笛卡儿叶形线的隐式方程为：
![x^3 + y^3 - 3 a x y = 0. \,](/Images/godic/202501/13/63c2d0f4651f93f5edb52fecfefcbb3e3137.png")
在极坐标中的方程为：
![r = \frac{3 a \sin \theta \cos \theta}{\sin^3 \theta + \cos^3 \theta }.](/Images/godic/202501/13/6c52c710c013bc29543f201902b364c03137.png")
这个名字来自 拉丁文 的 folium ，意思是 "leaf"（叶子）。
Folium of Descartes
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Folium of Descartes 笛卡儿叶形线
![The folium of Descartes (green) with asymptote (blue).](/Images/godic/202501/13/Kartesisches-Blatt.svg3138.png")
In geometry, the folium of Descartes is an algebraic curve defined by the equation
It forms a loop in the first quadrant with a double point at the origin and asymptote
It is symmetrical about ![y = x](/Images/godic/202501/13/5dbad057040ec6eb5aa5841786e25d333138.png")
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The name comes from the Latin word folium which means "leaf".