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玫瑰线

2009-08-03 21:56:03| 分类：高等数学图形动画 | 标签： |举报 |字号大中小订阅

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在极坐标系中，以下方程表示的曲线称为玫瑰线（Rose curve）:

或

当 n 是奇数时，玫瑰线有 n 个花瓣，称为 n 叶玫瑰。

当 n 是偶数时，玫瑰线有 2n 个花瓣，为 2n 叶玫瑰。

注：当 n 是分数或无理数时，图形要复杂一些，详见 Rose curve。

三叶玫瑰

with(plots):a:=1:
curve:=polarplot(a*sin(3*theta),thickness=3):
display(curve,scaling=constrained,title="three-leaved rose curve",tickmarks=[0,0]);

四叶玫瑰

with(plots):a:=1:
curve:=polarplot(a*sin(2*theta),thickness=3):
display(curve,scaling=constrained,title="four-leaved rose curve",tickmarks=[0,0]);

五叶玫瑰

with(plots):a:=1:
curve:=polarplot(a*cos(5*theta),thickness=3):
display(curve,scaling=constrained,title="five-leaved rose curve",tickmarks=[0,0]);

八叶玫瑰

with(plots):a:=1:
curve:=polarplot(a*cos(4*theta),thickness=3):
display(curve,scaling=constrained,title="eight-leaved rose curve",tickmarks=[0,0]);

二十叶玫瑰

with(plots):a:=1:
curve:=polarplot(a*sin(10*theta),thickness=3):
display(curve,scaling=constrained,title="twenty-leaved rose curve",tickmarks=[0,0]);

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