帕斯卡蜗线 Limaçon



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的圆,从圆周上任意一定点
引射线
,交圆于点
。在
上,从点
分别向两侧截取长度为b的线段
和
,当射线
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
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”。
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)
![]() ![]() ![]() 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
英语百科
Limaçon 帕斯卡蜗线(重定向自Limacon of Pascal)
![]() ![]() ![]() 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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