Kuen 曲面

几何画板及绘图内容加载中，请稍等……

2015-02-04 22:11

函数解析几何参数方程

这个范例演示了Kuen曲面，这是一种双曲几何中的特殊曲面。它涉及双曲几何和分段函数的概念。通过使用Surface, Sequence等GeoGebra命令，可以动态地展示曲面的构造过程。适合大学数学课程中的微积分和几何学教学。

GeoGebra 命令及参数

Surface((((2 * (cos(u) + (u * sin(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), (((2 * (sin(u) - (u * cos(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), (log(tan((1 / 2 * v))) + ((2 * cos(v))) / (1 + (u^(2) * sin(v)^(2)))) / c, u, 0, b, v, 0.02, 3.13) → a
Sequence(CurveCartesian[(((2 * (cos(u) + (u * sin(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), (((2 * (sin(u) - (u * cos(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), (log(tan((1 / 2 * v))) + ((2 * cos(v))) / (1 + (u^(2) * sin(v)^(2)))) / c, u, 0, b], v, 0.02, 3.13, 3.11 / n) → liste1
Sequence(CurveCartesian[(((2 * (cos(u) + (u * sin(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), (((2 * (sin(u) - (u * cos(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), (log(tan((1 / 2 * v))) + ((2 * cos(v))) / (1 + (u^(2) * sin(v)^(2)))) / c, v, 0.02, 3.13], u, 0, b, b / n) → liste2
Surface((((2 * (cos(u) + (u * sin(u)))) * sin(v))) / (1 + (u^(2) * sin(v)^(2))), ((-(((2 * (sin(u) - (u * cos(u)))) * sin(v))))) / (1 + (u^(2) * sin(v)^(2))), (log(tan((1 / 2 * v))) + ((2 * cos(v))) / (1 + (u^(2) * sin(v)^(2)))) / c, u, 0, b, v, 0.02, 3.13) → d