积极 AI Logo 积极 AI

隐函数与显函数交点

隐函数与显函数交点
几何画板及绘图内容加载中，请稍等……
2016-08-22 21:38
函数三角函数解析几何立体几何函数图像
所属专题 intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
该范例演示了隐函数 f(x,y,z) = cos(x) + cos(y) + cos(z) = 0 与显函数 z = x^2 - y^2 的交点。涉及的核心数学概念包括隐函数、显函数、三维空间中的曲面交点。使用了 If, Polygon, Textfield, Point, Zip, ImplicitCurve, IntersectPath, Sequence 等 GeoGebra 命令。适合高中及以上学生或教师使用，用于教学三维几何中的曲面交点问题。

GeoGebra 命令及参数

  1. If(Length[RemoveUndefined[Join[Zip[Mirror[{Roots[f01(a, x), y_{min}, y_{max}]}, y = x] + (a, 0), a, Sequence[x_{min} + ((x_{max} - x_{min}) / N_P * i), i, 0, N_P]]]]] ≟ 0, false, true) → lb1
  2. If(lb1, RemoveUndefined[Join[Zip[Mirror[{Roots[f01(a, x), y_{min}, y_{max}]}, y = x] + (a, 0), a, Sequence[x_{min} + ((x_{max} - x_{min}) / N_P * i), i, 0, N_P]]]], Sequence[(10000, 10000), k, 1, 50]) → P1xxy
  3. If(lb1, RemoveUndefined[Join[Zip[Reverse[{Roots[f01(x, a), x_{min}, x_{max}]}] + (0, a), a, Sequence[y_{min} + ((y_{max} - y_{min}) / N_P * i), i, 0, N_P]]]], Sequence[(10000, 10000), k, 1, 50]) → P2yyx
  4. Polygon((x_{min}, y_{min}), (x_{max}, y_{min}), (x_{max}, y_{max}), (x_{min}, y_{max})) → poly1, b, c, d, e
  5. Textfield(x_{min}) → inputBox4
  6. Textfield(x_{max}) → inputBox5
  7. Textfield(y_{max}) → inputBox6
  8. Textfield(z_{max}) → inputBox7
  9. Textfield(y_{min}) → inputBox8
  10. Textfield(z_{min}) → inputBox9
  11. Textfield(N_P) → inputBox10
  12. Textfield(zoom_{3D}) → InputBox1
  13. Point(Pxy) → D
  14. Textfield(u) → InputBox4
  15. Textfield(f) → inputBox3
  16. Zip((x(a), y(a), u(x(a), y(a))), a, Join[{P1xxy, P2yyx}]) → list1
  17. ImplicitCurve(f01) → pp
  18. IntersectPath(Z_0, f(x, y, z0) + z0) → ic2z
  19. Textfield(t) → InputBox2
  20. Sequence(Sequence[(i * acos((-cos(x)) - cos(y))) + ((j * 2) * π), i, -1, 1, 2], j, -2, 2) → l_f