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圆锥截面演示 by amit.quackenbush

圆锥截面演示 by amit.quackenbush
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2017-04-07 19:07
三角函数立体几何几何作图
①本范例演示圆锥的截面图形变化；②涉及核心数学概念包括立体几何、三角函数、导数和极限；③构造要点：使用Vector（向量）、OrthogonalLine（垂线）、Translate（平移）、Mirror（镜像）、Polygon（多边形）、Midpoint（中点）、Conic（圆锥曲线）、Segment（线段）、Line（直线）、Point（点）、Intersect（交点）、AngularBisector（角平分线）等GeoGebra命令和对象；④适合高中及以上学生及数学爱好者学习圆锥截面性质及几何作图。

GeoGebra 命令及参数

  1. Vector(B_1, X) → u
  2. Vector(B_1, Z) → w
  3. OrthogonalLine(Vues, yAxis) → a
  4. OrthogonalLine(Vues, xAxis) → b
  5. Vector(B_1, Y) → v
  6. Translate(O, Vector[(R * u)]) → O'_1
  7. Translate(O, Vector[(R * v)]) → O'_2
  8. Mirror(O'_2, O) → O''
  9. Mirror(O'_1, O) → A
  10. Polygon(A, O'_2, O'_1, O'') → poly1, a_1, o', o'_1, o''
  11. Midpoint(a_1) → B
  12. Midpoint(o'') → C
  13. Midpoint(o'_1) → D
  14. Midpoint(o') → E
  15. Conic(E, B, C, D, E) → d
  16. Midpoint(O, O'_2) → F
  17. Midpoint(F, B) → G
  18. Midpoint(O, G) → H
  19. Midpoint(O, G) → I
  20. Midpoint(G, I) → J
  21. Mirror(J, G) → J'
  22. Conic(E, J', B, C, D) → e
  23. Translate(O, Vector[(h * w)]) → S
  24. Segment(S, O) → f
  25. Line(O'_2, f) → i
  26. Line(A, f) → j
  27. Line(O'', f) → l
  28. Point(j) → K
  29. Point(i) → L
  30. Point(l) → M
  31. Segment(K, L) → m
  32. Segment(K, M) → n
  33. Line(L, n) → p
  34. Line(M, m) → q
  35. Intersect(p, q) → N
  36. Polygon(K, L, N, M) → poly2, k_1, l_1, n_1, m_1
  37. Midpoint(k_1) → P
  38. Midpoint(l_1) → Q
  39. Midpoint(m_1) → S_2
  40. Midpoint(n_1) → T
  41. Line(S, E) → r
  42. Line(B, S) → s
  43. Line(S, D) → t
  44. Line(S, C) → b_1
  45. Line(S_2, Q) → c_1
  46. Line(P, T) → d_1
  47. Intersect(c_1, r) → U
  48. Intersect(c_1, b_1) → V
  49. Intersect(s, d_1) → W
  50. Intersect(t, d_1) → A_1
  51. Segment(S, D) → e_1
  52. Segment(S, C) → f_1
  53. Segment(S, B) → g_1
  54. Segment(S, E) → h_1
  55. Line(V, m_1) → i_1
  56. Line(W, k_1) → j_1
  57. Line(U, l_1) → p_1
  58. Line(A_1, n_1) → q_1
  59. Intersect(p_1, j_1) → C_1
  60. Intersect(i_1, j_1) → D_1
  61. Intersect(q_1, i_1) → E_1
  62. Intersect(q_1, p_1) → F_1
  63. Polygon(D_1, C_1, F_1, E_1) → poly3, d_2, c_2, f_2, e_2
  64. Midpoint(C_1, E_1) → G_1
  65. Mirror(V, G_1) → V'
  66. Conic(U, V', W, V, A_1) → r_1
  67. Segment(O'_1, A) → s_1
  68. Segment(O'_2, O'') → t_1
  69. Intersect(e, s_1) → H_1, I_1
  70. Intersect(e, t_1) → J_1, K_1
  71. Segment(S, I_1) → a_2
  72. Segment(S, J_1) → b_2
  73. Segment(S, H_1) → g_2
  74. Segment(S, K_1) → h_2
  75. AngularBisector(O'_2, O, B) → i_2
  76. AngularBisector(A, O, B) → j_2
  77. AngularBisector(C, O, A) → k_2
  78. AngularBisector(O'', O, C) → l_2
  79. Midpoint(B, A) → L_1
  80. Midpoint(O'_2, B) → M_1
  81. Midpoint(O'_2, E) → N_1
  82. Midpoint(A, C) → O_1
  83. Line(O, L_1) → m_2
  84. Line(N_1, O) → n_2
  85. Line(M_1, O) → p_2
  86. Line(O_1, O) → q_2
  87. Intersect(e, p_2) → P_1, Q_1
  88. Intersect(e, m_2) → R_1, S_1
  89. Intersect(e, q_2) → T_1, U_1
  90. Intersect(e, n_2) → V_1, W_1
  91. Segment(Q_1, S) → r_2
  92. Segment(W_1, S) → s_2
  93. Segment(T_1, S) → t_2
  94. Segment(S_1, S) → a_3
  95. Segment(R_1, S) → b_3
  96. Segment(U_1, S) → c_3
  97. Segment(S, V_1) → d_3
  98. Segment(P_1, S) → e_3
  99. Intersect(e, r_1) → Z_1, A_2, B_2, C_2
  100. Conic(E, J', B, C, D) → f_3
  101. Conic(U, V', W, V, A_1) → g_3
  102. Polygon(K, L, N, M) → poly4, k_3, l_3, n_3, m_3
  103. Polygon(A, O'_2, O'_1, O'') → poly5, a_4, o'_2, o'_3, o''_1