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圆锥交集演示

圆锥交集演示
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2018-12-15 03:43
函数解析几何立体几何微积分几何作图
①本范例演示圆锥的交集图形/现象；②涉及核心数学概念包括圆锥、交集、百分比、二次函数、定积分、斜率、算术；③作图要点提炼自构造摘要，使用了Intersect（交集）、Circle（圆）、Point（点）、OrthogonalLine（垂线）、Segment（线段）、Rotate（旋转）、Angle（角度）、Ray（射线）、Locus（轨迹）、Mirror（镜像）、CircleArc（圆弧）等GeoGebra命令/对象；④适合高中及以上学段，用于立体几何和微积分教学。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, r1) → c
  3. Circle(A, d) → e
  4. Intersect(e, xAxis, 2) → B
  5. Circle(B, r2) → f
  6. Point(yAxis) → C
  7. OrthogonalLine(C, yAxis) → g
  8. Intersect(c, xAxis) → D, E
  9. Intersect(f, xAxis) → F, G
  10. OrthogonalLine(D, xAxis) → h
  11. OrthogonalLine(F, xAxis) → i
  12. OrthogonalLine(E, xAxis) → j
  13. OrthogonalLine(B, xAxis) → k
  14. OrthogonalLine(G, xAxis) → l
  15. Intersect(g, h) → H
  16. Intersect(g, i) → I
  17. Intersect(g, j) → J
  18. Intersect(g, k) → K
  19. Intersect(g, l) → L
  20. Circle(C, h1) → p
  21. Intersect(p, yAxis, 2) → M
  22. Circle(K, h2) → q
  23. Intersect(q, k, 2) → N
  24. Segment(M, H) → m
  25. Segment(M, J) → n
  26. Segment(N, I) → r
  27. Segment(N, L) → s
  28. Point(xAxis) → O
  29. Rotate(A, (-(45°)), O) → A'
  30. Angle(A', O, A) → α
  31. Ray(A', O) → t
  32. Point(t) → P
  33. Ray(P, O) → a
  34. Intersect(c, f) → Q, R, ,
  35. OrthogonalLine(Q, yAxis) → b
  36. OrthogonalLine(R, yAxis) → f_1
  37. Intersect(a, b) → S
  38. Intersect(f_1, a) → T
  39. OrthogonalLine(S, xAxis) → g_1
  40. OrthogonalLine(T, xAxis) → h_1
  41. Intersect(g, g_1) → U
  42. Intersect(g, h_1) → V
  43. Intersect(n, r) → W
  44. OrthogonalLine(W, g) → i_1
  45. Intersect(i_1, xAxis) → Z
  46. OrthogonalLine(W, yAxis) → j_1
  47. OrthogonalLine(O, xAxis) → k_1
  48. Intersect(j_1, k_1) → A_1
  49. Intersect(g, i_1) → B_1
  50. Segment(W, B_1) → l_1
  51. Point(l_1) → C_1
  52. OrthogonalLine(C_1, yAxis) → m_1
  53. Intersect(m_1, r) → D_1
  54. Intersect(m_1, n) → E_1
  55. OrthogonalLine(E_1, m_1) → n_1
  56. OrthogonalLine(D_1, m_1) → p_1
  57. Intersect(p_1, xAxis) → F_1
  58. Intersect(n_1, xAxis) → G_1
  59. Circle(A, G_1) → c_1
  60. Circle(B, F_1) → d_1
  61. Intersect(d_1, c_1) → H_1, I_1, ,
  62. OrthogonalLine(I_1, yAxis) → q_1
  63. OrthogonalLine(H_1, yAxis) → r_1
  64. Intersect(q_1, a) → J_1
  65. Intersect(r_1, a) → K_1
  66. OrthogonalLine(J_1, xAxis) → s_1
  67. OrthogonalLine(K_1, xAxis) → t_1
  68. Intersect(m_1, s_1) → L_1
  69. Intersect(m_1, t_1) → M_1
  70. Locus(L_1, C_1) → lieu1
  71. Locus(M_1, C_1) → lieu2
  72. OrthogonalLine(N_1, xAxis) → a_1
  73. Circle(N_1, a1) → e_1
  74. Intersect(e_1, a_1, 1) → O_1
  75. Rotate(O_1, α1, N_1) → P_1
  76. Angle(O_1, N_1, P_1) → β
  77. Mirror(P_1, a_1) → Q_1
  78. CircleArc(N_1, Q_1, P_1) → c_2
  79. Segment(N_1, P_1) → b_1
  80. Segment(N_1, Q_1) → f_2
  81. Locus(I_1, C_1) → lieu3
  82. Locus(H_1, C_1) → lieu4
  83. CircleArc(A, G_1, I_1) → arc
  84. Segment(M, E_1) → ai
  85. Circle(N_1, ai) → d_2
  86. Rotate(O_1, (360° * arc / ((π * ai))), N_1) → R_1
  87. Angle(O_1, N_1, R_1) → γ
  88. Segment(N_1, R_1) → g_2
  89. Intersect(d_2, g_2, 1) → S_1
  90. Locus(S_1, C_1) → lieu5
  91. Mirror(S_1, a_1) → T_1
  92. Locus(T_1, C_1) → lieu6