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可调节的菱形截面平行于y轴的定制立体

可调节的菱形截面平行于y轴的定制立体
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2019-04-05 10:22
函数解析几何立体几何
所属专题 GeoGebra 3D & AR: PreCalc & Calculus Resources Cross Sectional Specials (Calculus)
这个范例演示了一个可调节的立体，其截面平行于y轴的形状为菱形。核心数学概念包括函数、解析几何和立体几何。构造过程中使用了GeoGebra的Intersect（相交）、Line（直线）、Segment（线段）、Rotate（旋转）、Translate（平移）、Midpoint（中点）、Sphere（球体）、Textfield（文本框）、Polygon（多边形）、CurveCartesian（笛卡尔曲线）、Surface（曲面）和Angle（角度）等命令和对象。适合高中及以上学生学习和理解函数图像与立体几何的关系，以及如何通过参数调节图形特性。

GeoGebra 命令及参数

  1. Intersect(lower, h, (0, -8)) → C
  2. Line(C, C + (1, 0, 0)) → c
  3. Intersect(upper, h, (0, 4)) → B
  4. Segment(C, B) → q
  5. Intersect(upper, q, (0, 4)) → G
  6. Rotate(G, (ANG * pi / 180), C, c) → G'_1
  7. Translate(G'_1, Vector[C, G]) → J_1
  8. Segment(H, I) → s_1
  9. Midpoint(s_1) → A_1
  10. Segment(J, K) → q_1
  11. Midpoint(q_1) → Z
  12. Midpoint(s_1) → E
  13. Midpoint(q_1) → F
  14. Midpoint(C, G) → T
  15. Line(B, D) → i
  16. Sphere(B, d) → e
  17. Segment(C, B) → p
  18. Textfield(upper) → InputBox1
  19. Textfield(lower) → InputBox2
  20. Textfield(a) → InputBox3
  21. Textfield(b) → InputBox4
  22. Segment(C, G) → k_1
  23. Line(C, G) → j
  24. Sphere(G, T) → k
  25. Line(T, T + (1, 0, 0)) → m
  26. Rotate(G, pi / 3, F_1, m) → G'
  27. Rotate(G', pi / 3, F_1, Line[F_1, F_1 + (1, 0, 0)]) → G''
  28. Line(F_1, F_1 + (1, 0, 0)) → n
  29. Rotate(G'', pi / 3, F_1, n) → G'''
  30. Rotate(G''', pi / 3, F_1, n) → G_1
  31. Polygon(C, G, J_1, G'_1) → poly1, g_1, m_1, r_1, a_1
  32. Line(Z, Z + (1, 0, 0)) → f
  33. Line(D_1, D_1 + (1, 0, 0)) → g
  34. Rotate(J, pi / 3, D_1, g) → J'
  35. Rotate(J', pi / 3, D_1, g) → J''
  36. Rotate(J'', pi / 3, D_1, g) → J'''
  37. Rotate(J''', pi / 3, D_1, g) → E_1
  38. Line(H_1, H_1 - (1, 0, 0)) → l_1
  39. Rotate(I, pi / 3, H_1, l_1) → I'
  40. Rotate(I', pi / 3, H_1, l_1) → I''
  41. Rotate(I'', pi / 3, H_1, l_1) → I'''
  42. Rotate(I''', pi / 3, H_1, l_1) → I_1
  43. Segment(G, J_1) → l
  44. Segment(J_1, G'_1) → r
  45. Segment(G'_1, C) → s
  46. Line(K, K + (1, 0, 0)) → t
  47. Rotate(J, (ANG * pi / 180), K, t) → J'_1
  48. Translate(J'_1, Vector[K, J]) → K_1
  49. Polygon(K, J, K_1, J'_1) → q1, k_3, j_1, k_4, j'_1
  50. Line(I, I + (1, 0, 0)) → f_1
  51. Rotate(H, (ANG * pi / 180), I, f_1) → H'
  52. Translate(H', Vector[I, H]) → H''
  53. Segment(H, H'') → i_1
  54. Segment(H'', H') → n_1
  55. Segment(H', I) → p_1
  56. Polygon(I, H, H'', H') → q2, i_2, h_2, h'', h'
  57. Segment(J, K_1) → b_1
  58. Segment(K_1, J'_1) → c_1
  59. Intersect(t, q_1) → L_1
  60. Segment(J'_1, L_1) → d_1
  61. CurveCartesian(t, lower(t) + ((upper(t) - lower(t)) * cos((ANG * pi / 180))), ((upper(t) - lower(t)) * sin((ANG * pi / 180))), t, a, b) → o
  62. CurveCartesian(t, upper(t) + ((upper(t) - lower(t)) * cos((ANG * pi / 180))), ((upper(t) - lower(t)) * sin((ANG * pi / 180))), t, a, b) → u
  63. Surface(u, lower(u) + (((upper(u) - lower(u)) * v) * cos((ANG * pi / 180))), (((upper(u) - lower(u)) * v) * sin((ANG * pi / 180))), u, a, b, v, 0, 1) → v
  64. Surface(u, lower(u) + ((upper(u) - lower(u)) * cos((ANG * pi / 180))) + (v * (upper(u) - lower(u))), ((upper(u) - lower(u)) * sin((ANG * pi / 180))), u, a, b, v, 0, 1) → w
  65. Surface(u, upper(u) + (((upper(u) - lower(u)) * v) * cos((ANG * pi / 180))), (((upper(u) - lower(u)) * v) * sin((ANG * pi / 180))), u, a, b, v, 0, 1) → e_1
  66. Angle(G, C, G'_1) → α