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棱锥截体演示

棱锥截体演示
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2020-05-02 00:29
解析几何立体几何概率统计不等式几何作图
①本范例演示棱锥截体的几何构造与性质；②涉及核心数学概念包括棱锥体积计算、重心（质心）定位、解析几何作图、条件概率与不等式应用；③构造过程中运用了Intersect（交点）、Polygon（多边形）、Pyramid（棱锥）、Centroid（重心）、Segment（线段）、Translate（平移）、Midpoint（中点）等GeoGebra命令与对象；④适合高中及以上数学教学，用于立体几何、解析几何及概率统计的综合应用教学。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → C
  2. Polygon(C, C', N, xOyPlane) → poly1, j, D, F, I, J, K, k, m, n, f, i, p, q, B
  3. Pyramid(poly1, h_1) → a, A_2, edgeAC, edgeAC', edgeAB, edgeAD, edge1, edge2, edge3, edge4, faceACC', faceABC', faceABD, faceACD, face1, face2, face3, face4
  4. Centroid(poly1) → E
  5. Segment(C, C') → l_1
  6. IntersectPath(r, faceABC') → g
  7. Intersect(r, faceABC') → G, L
  8. IntersectPath(r, faceACC') → h
  9. Intersect(r, faceACC') → M, O
  10. IntersectPath(r, a) → poly2, P, b, c, d, m_1, f_1, g_1, i_1, Q, R, S, T, U, V, W, s
  11. Pyramid(poly2, A_2) → e, faceAPQ, edgeAQ, edgeAR, edgeAS, edge5, edge6, edge7, edge8, faceAQR, faceARS, faceAPS, face5, face6, face7, face8, edgeAP
  12. Segment(E, Z) → j_1
  13. Segment(S, D) → n_1
  14. Segment(A, C) → r_1
  15. Segment(A_2, E) → q_1
  16. Segment(A_2, Z) → s_1
  17. Translate(e, Vector[(t * u)]) → e'
  18. Translate(A_2, Vector[(t * u)]) → A'
  19. Translate(A_2, Vector[(t * u)]) → A'_1
  20. Translate(Z, Vector[(t * u)]) → Z'
  21. Segment(A'_1, Z') → t_1
  22. Translate(Z, Vector[(t * u)]) → Z'_1
  23. Translate(S, Vector[(t * u)]) → S'
  24. Segment(A_2, S) → b_1
  25. Translate(A_2, Vector[(t * u)]) → A'_2
  26. Translate(S, Vector[(t * u)]) → S'_1
  27. Segment(A'_2, S'_1) → c_1
  28. Segment(A_2, M) → d_1
  29. Polygon(C', B, L, G) → q1, c', b_2, l_2, g_2
  30. Polygon(B, D, S, L) → q2, b_3, d_2, s_2, l_3
  31. Polygon(D, S, T, F) → q3, d_3, s_3, t_2, f_2
  32. Polygon(T, U, I, F) → q4, t_3, u_1, i_2, f_3
  33. Polygon(I, C, M, U) → q5, i_3, c_2, m_2, u_2
  34. Polygon(C, C', G, M) → q6, c_3, h_2, g_3, m_3
  35. Polygon(B, D, S, L) → q7, b_4, d_4, s_4, l_4
  36. Polygon(B, C', G, L) → q8, b_5, n_2, g_4, l_5
  37. Polygon(C', C, M, G) → q9, p_2, c_4, m_4, g_5
  38. Polygon(M, C, J, V) → q10, m_5, c_5, j_3, v_1
  39. Polygon(J, I, U, V) → q11, j_4, i_4, u_3, v_2
  40. Polygon(U, T, F, I) → q12, u_4, t_4, f_4, i_5
  41. Polygon(F, D, S, T) → q13, f_5, d_5, s_5, t_5
  42. Polygon(B, D, S, L) → q14, b_6, d_6, s_6, l_6
  43. Polygon(B, C', G, L) → q15, b_7, a_2, g_6, l_7
  44. Polygon(C', C, M, G) → q16, e_2, c_6, m_6, g_7
  45. Polygon(C, K, W, M) → q17, c_7, k_3, w_1, m_7
  46. Polygon(D, F, T, S) → q18, d_7, f_6, t_6, s_7
  47. Polygon(F, I, U, T) → q19, f_7, i_6, u_5, t_7
  48. Polygon(I, J, V, U) → q20, i_7, j_5, v_3, u_6
  49. Polygon(K, J, V, W) → q21, k_4, j_6, v_4, w_2
  50. Polygon(C', B, L, G) → q22, p_3, b_8, l_8, g_8
  51. Polygon(B, D, S, L) → q23, b_9, d_8, s_8, l_9
  52. Polygon(D, F, T, S) → q24, d_9, f_8, t_8, s_9
  53. Polygon(C', C, M, G) → q25, q_3, c_8, m_8, g_9
  54. Polygon(L, G, C', B) → q28, l_{10}, g_{10}, e_3, b_{10}
  55. Polygon(C, C', G, M) → q29, c_{11}, h_4, g_{11}, m_{11}
  56. Polygon(D, B, L, S) → q30, d_{11}, b_{11}, l_{11}, s_{11}
  57. Segment(G, C') → p_4
  58. Segment(E, C) → a_3
  59. Segment(S, D) → a_4
  60. Segment(Z, E) → e_4
  61. Segment(D, S) → h_5
  62. Polygon(L, M, C, B) → q31, l_{12}, m_{12}, c_{12}, b_{12}
  63. Polygon(C', B, L, G) → q32, p_5, b_{13}, l_{13}, g_{12}
  64. Polygon(C, C', G, M) → q33, c_{13}, q_5, g_{13}, m_{13}
  65. Translate(poly2, Vector[(t * u)]) → poly2'
  66. Translate(T, Vector[(t * u)]) → T'
  67. Translate(U, Vector[(t * u)]) → U'
  68. Translate(V, Vector[(t * u)]) → V'
  69. Translate(W, Vector[(t * u)]) → W'
  70. Translate(M, Vector[(t * u)]) → M'
  71. Translate(G, Vector[(t * u)]) → G'
  72. Translate(L, Vector[(t * u)]) → L'
  73. Polygon(M, W, A) → t1, a_5, m_{14}, w_3
  74. Segment(Z, E) → r_5
  75. Segment(Z, E) → e_5
  76. Midpoint(M, G) → A_1
  77. Midpoint(C, C') → B_1
  78. Segment(A_1, B_1) → h_6
  79. Segment(S, D) → k_6
  80. Segment(A, B_1) → k_1
  81. Segment(A, A_1) → n_5
  82. Translate(A, Vector[(t * u)]) → A'_{3}
  83. Translate(A_1, Vector[(t * u)]) → C_1
  84. Segment(A'_{3}, C_1) → n_6
  85. Translate(Q, Vector[(t * u)]) → Q'
  86. Translate(A_2, Vector[(t * u)]) → D_1
  87. Translate(E, Vector[(t * u)]) → E'
  88. Translate(C', Vector[(t * u)]) → C''
  89. Translate(Z, Vector[(t * u)]) → Z'_{2}
  90. Translate(G, Vector[(t * u)]) → G'_{1}
  91. Translate(M, Vector[(t * u)]) → M'_{1}
  92. Translate(Z, Vector[(t * u)]) → Z'_{3}
  93. Segment(M'_{1}, Z'_{3}) → a_1
  94. Segment(A'_{3}, M'_{1}) → p_6
  95. Segment(M, Z) → r_3
  96. Segment(C, E) → n_3
  97. Point(m_2) → E_1
  98. Segment(A, E_1) → p_1
  99. Point(t_3) → F_1
  100. Segment(A, F_1) → e_1
  101. Segment(A, U) → j_2
  102. Segment(A, V) → k_2

AI 绘图提示语参考

画一个截锥体，展示其几何构造和性质。首先绘制底面和顶面，然后连接顶点形成侧面。标出底面和顶面的中心点，并画出中心点之间的连线。接着，在截锥体上随机选择一点，并画出该点与顶面和底面的交线。最后，将截锥体沿中心点连线进行平移，展示平移后的截锥体。
以上提示语为根据原始绘图命令整理而来，仅供参考。