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玻璃杯中的球体

玻璃杯中的球体
几何画板及绘图内容加载中，请稍等……
2016-01-02 01:43
三角函数立体几何几何作图函数图像
①本范例演示了球体在玻璃杯中部分浸入水面的几何现象；②涉及的核心数学概念包括体积计算、球体表面积、百分比、自然数等；③作图要点提炼自构造摘要，使用了RotateText, Circle, Sphere, Cylinder, Intersect等GeoGebra命令和对象；④适合高中阶段学生学习立体几何、体积计算及空间想象能力。

GeoGebra 命令及参数

  1. RotateText("uStas\;\&\,Т.С.", 90°) → надпись01
  2. Circle(Q - (0, 0, 2), 0.4, zAxis) → ϕ
  3. Cone(ϕ, 2) → d, c, a_1
  4. Segment(A, B) → plechy
  5. Segment(A, A_1) → a
  6. Segment(B, B_1) → b
  7. Circle(A_1, m, zAxis) → ω_a
  8. Cylinder(ω_a, (2 * m)) → φ_a, ω'_a, a_a
  9. Circle(B_1, m, zAxis) → ω_b
  10. Cylinder(ω_b, (2 * m)) → φ_b, ω'_b, a_b
  11. Sphere(A_1 + (0, 0, R), R) → ψ_a
  12. Sphere(B_1 + (0, 0, R), R) → ψ_b
  13. Line(A_2 + (0, 0, (0.5 * p)), xAxis) → d_a
  14. Line(B_2 + (0, 0, (0.5 * p)), xAxis) → d_b
  15. Parabola(F_a, d_a) → λ_a
  16. Parabola(F_b, d_b) → λ_b
  17. Intersect(Line[A_1 + (0, 0, h), xAxis], λ_a, 2) → G_a
  18. Intersect(Line[B_1 + (0, 0, h), xAxis], λ_b, 1) → G_b
  19. CurveCartesian(x(A_2) - i, 0, z(A_2) - (0.5 * i^(2) / p), i, 0, ii) → θ_a
  20. CurveCartesian(x(B_2) + i, 0, z(B_2) - (0.5 * i^(2) / p), i, 0, ii) → θ_b
  21. Cylinder(ω_a, h) → ϕ_a, ω''_a, i
  22. Intersect(f, xAxis, 2) → F
  23. IntersectPath(z = z(B_1) + h_3, ψ_b) → θ
  24. Point(θ, 0.5) → U
  25. Surface(x(A_1) + ((R * sin(i)) * sin(j)), y(A_1) + ((R * sin(i)) * cos(j)), z(A_1) + R + (R * cos(i)), i, α_1, (2 * π) - α_1, j, 0, 6.2831853072) → ψ'_a
  26. Surface(x(A_1) + ((R * sin(i)) * sin(j)), y(A_1) + ((R * sin(i)) * cos(j)), z(A_1) + R + (R * cos(i)), i, 1.5707963267948966, 4.71238898038469, j, 0, 3.141592653589793) → ψ''_a
  27. Surface(x(A_1) + ((R * sin(i)) * sin(j)), y(A_1) + ((R * sin(i)) * cos(j)), z(A_1) + R + (R * cos(i)), i, π - α_1, π + α_1, j, 0, 6.2831853072) → ψ'''_a
  28. Cylinder(ω''_a, h') → ϕ'_a, ω'''_a, g
  29. Cylinder(ω_b, (h' * h_3 / h_4)) → ϕ_b, ω''_b, j
  30. Sphere(B_3, R) → ψ'_b
  31. Translate(θ, Vector[(0, 0, h_5 + (1.5 * p))]) → θ'
  32. Cylinder(ω_b, (h' * h_3 / h_4) + h_5 + (1.5 * p)) → ϕ'_b, e, k
  33. Translate(U, Vector[B_1, A_1]) → U_a
  34. Circle(A_1 + (0, 0, z(U_a) - z(A_1)), Radius[θ], zAxis) → θa