三维空间中圆柱与球体的交集

几何画板及绘图内容加载中，请稍等……

2014-04-24 20:34

解析几何立体几何几何作图

本范例演示了在三维空间中，圆柱沿x、y、z轴方向的展开，以及以原点为中心的球体。核心数学概念包括立体几何中的圆柱和球体。通过Surface命令构造了圆柱和球体的表面，以及它们的交集。适合高中及以上学生学习立体几何。

GeoGebra 命令及参数

Surface(4 + cos(b), 3 + sin(b), 2 + (5 * sin(a)), a, 0, 3.141592653589793, b, 0, 3.141592653589793) → cil2_z
Surface(4 + (2 * cos(b)), 5 + (2 * sin(b)), 2 + (5 * sin(a)), a, 0, 3.141592653589793, b, 0, 6.28319) → cil_z
Surface(((7 * sin(a)) * cos(a)), sin(b), cos(b), a, 0, 6.28319, b, 0, 6.28319) → cil_x
Surface(sin(a), (7 * cos(b)), cos(a), a, 0, 6.28319, b, 0, 6.28319) → cil_y
Surface(((2.5 * cos(u)) * cos(v)), ((2.5 * sin(u)) * cos(v)), (2.5 * sin(v)), u, 0, 6.28319, v, 0, 6.28319) → sfera_{0,0,0}
Surface((7 * sin(a)), sin(b), cos(b), a, 0, 6.283185307179586, b, 0, 6.283185307179586) → cil'_x
Surface(10 + (sin(a) * sin(b)), 10 + (sin(b) * cos(a)), 10 + cos(b), a, 0, 3.141592653589793, b, 0, 3.141592653589793) → sfera_{xyz}
Surface((1.5 * cos(a)), (5 * sin(b)), (1.5 * sin(a)), a, 0, 6.28319, b, 0, 6.28319) → cil'_y