环面与平面的交线

几何画板及绘图内容加载中，请稍等……

2017-07-24 19:16

所属专题 intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve

这个范例演示了环面与平面的交线。涉及的核心数学概念包括立体几何和解析几何。通过使用GeoGebra命令如Surface、CurveCartesian、IntersectPath等，可以构造出环面和平面的交线。适合高中数学教学和学习使用。

GeoGebra 命令及参数

Circle(O, R, xOyPlane) → midtor
Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, (2 * π), v, 0, (2 * π)) → Torus
CurveCartesian(x(Q) - (sin(α) * u), y(Q) + (cos(α) * u), u, -10, 10) → αline
Surface(x(Q) + (sin(α) * t) - ((sin(ϕ) * cos(α)) * w), y(Q) - (cos(α) * t) - ((sin(ϕ) * sin(α)) * w), z(Q) + (w * cos(ϕ)), t, -10, 10, w, -10, 10) → s
Vector(Q, Q + (sin(α), (-cos(α)), 0)) → t_{axis}
Vector(Q, Q + (((-cos(α)) * sin(ϕ)), ((-sin(α)) * sin(ϕ)), cos(ϕ))) → w_{axis}
Circle(O, R + r, xOyPlane) → exttor
Circle(O, R - r, xOyPlane) → intttor
Line(Q, t_{axis}) → tline
Line(Q, w_{axis}) → wline
IntersectPath(xypla, αϕQpla) → f
ImplicitCurve(torus(x, (ρ * cos(ϕ)) - (y * sin(ϕ)), z(Q) + (y * cos(ϕ)))) → ftw