The 渐伸线 of the 星形线 is a hypocycloid involute for 
. Surprisingly, it is another 星形线 scaled by a factor 
and rotated 
of a turn. For an 星形线 with parametric equations
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  | ![1/8[3cost-cos(3t)]](/images/equations/AstroidInvolute/Inline12.svg) |
(3)
|
 |  | ![1/8[3sint+sin(3t)].](/images/equations/AstroidInvolute/Inline15.svg) |
(4)
|
星形线的渐伸线
参见
星形线, 星形线渐屈线, 渐伸线使用 Wolfram|Alpha 探索
引用为
Weisstein, Eric W. “星形线的渐伸线。” 来自 MathWorld——Wolfram Web 资源。 https://mathworld.net.cn/AstroidInvolute.html