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单词 Limacon of Pascal
释义

Limacon of Pascal

中文百科

帕斯卡蜗线 Limaçon

(重定向自Limacon of Pascal)
丢勒所画出的蜗线
三种帕斯卡蜗线
帕斯卡蜗线是圆的垂足曲线的演示

帕斯卡蜗线法语:Limaçon de Pascal),或直接称作蜗线,是一种平面曲线,若平面上有一直径为a的圆,从圆周上任意一定点O引射线OS,交圆于点Q。在OS上,从点Q分别向两侧截取长度为b的线段QP_1QP_2,当射线OS绕定点O旋转时,点P1、P2所形成的轨迹就叫做帕斯卡蜗线。帕斯卡蜗线的形状随\frac{a}{b}的值而变化,有时候是心脏线,有时候有内外两支,类似蜗牛壳,故被称作“limaçon”,这个词的本义是“小蜗牛”,源于拉丁语的 “limax”。

英语百科

Limaçon 帕斯卡蜗线

(重定向自Limacon of Pascal)
Three limaçons: dimpled, with cusp (a cardioid), and looped. Not shown: the convex limaçon
Limaçon — pedal curve of a circle

In geometry, a limaçon or limacon /ˈlɪməsɒn/, also known as a limaçon of Pascal, is defined as a roulette formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius. It can also be defined as the roulette formed when a circle rolls around a circle with half its radius so that the smaller circle is inside the larger circle. Thus, they belong to the family of curves called centered trochoids; more specifically, they are epitrochoids. The cardioid is the special case in which the point generating the roulette lies on the rolling circle; the resulting curve has a cusp.

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更新时间:2025/6/20 17:53:19