Oloide by Patrick Clément

几何画板及绘图内容加载中，请稍等……

2016-07-05 21:22

解析几何立体几何几何作图

该范例展示了Oloide这一几何体。涉及的核心数学概念包括立体几何和几何作图。通过使用Surface和CurveCartesian命令，构造了Oloide的表面和曲线。适合高中及以上学生或数学爱好者学习和探索。

GeoGebra 命令及参数

Surface(((d + (cos(u) * (1 - v)) + (v * ((-d) + 1 / (d + 1 / cos(u))))) * cos(a)) - ((sin(a) * v) * sqrt(1 - (1 / (d + 1 / cos(u)))^(2))), (sin(u) * (1 - v)), ((d + (cos(u) * (1 - v)) + (v * ((-d) + 1 / (d + 1 / cos(u))))) * sin(a)) + ((cos(a) * v) * sqrt(1 - (1 / (d + 1 / cos(u)))^(2))), u, (-π), π, v, 0, 1) → b
Surface(d + (cos(u) * (1 - v)) + (v * ((-d) + 1 / (d + 1 / cos(u)))), (sin(u) * (1 - v)), ((-v) * sqrt(1 - (1 / (d + 1 / cos(u)))^(2))), u, (-π), π, v, 0, 1) → j
CurveCartesian(d + cos(t), sin(t), 0, t, 0, (2 * π)) → c
CurveCartesian(cos(t), 0, sin(t), t, 0, (2 * π)) → e