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立方体两部分演示

立方体两部分演示
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2019-04-24 15:57
立体几何概率统计几何作图
所属专题 TWO PARTS OF A CUBE
①本范例演示立方体的不同部分及其几何关系；②涉及核心数学概念包括立体几何、表面积、相似三角形、相关性、正态分布和超几何分布；③作图要点使用了Point, Cube, Intersect, Line, Rotate, Midpoint, Prism等GeoGebra命令和对象；④适合高中及以上学生学习和理解复杂几何结构及概率统计应用。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD_1, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH_1, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Point(xAxis) → I
  6. Point(xAxis) → J
  7. Point(Circle[J, Distance[I, J], Segment[I, J]]) → K
  8. Cube(I, J, K) → b, L, faceKLPO, faceMNOP, edgeIL, edgeIJ, edgeJK_1, edgeKL, edgeIM, edgeLP, edgeMP, edgeMN, M, edgeJN, edgeNO, edgeKO, edgeOP, N, O, P, faceIJKL, faceILPM, faceIJNM, faceJKON
  9. Intersect(yAxis, xAxis) → Q
  10. Point(xAxis) → R
  11. Point(Circle[R, Distance[Q, R], Segment[Q, R]]) → S
  12. Cube(Q, R, S) → c, T, faceSTZW, faceUVWZ, edgeQT, edgeQR, edgeRS_1, edgeST, edgeQU, edgeTZ, edgeUZ, edgeUV, U, edgeRV, edgeVW, edgeSW, edgeWZ, V, W, Z, faceQRST, faceQTZU, faceQRVU, faceRSWV
  13. Point(xAxis) → A_1
  14. Point(xAxis) → B_1
  15. Point(Circle[B_1, Distance[A_1, B_1], Segment[A_1, B_1]]) → C_1
  16. Cube(A_1, B_1, C_1) → d, D_1, face5, face6, edge2, edge1, edge4, edge6, edge3, edge8, edge10, edge9, E_1, edge5, edge11, edge7, edge12, F_1, G_1, H_1, face1, face3, face2, face4
  17. Point(xAxis) → I_1
  18. Point(xAxis) → J_1
  19. Point(Circle[J_1, Distance[I_1, J_1], Segment[I_1, J_1]]) → K_1
  20. Cube(I_1, J_1, K_1) → e, L_1, face11, face12, edge14, edge13, edge16, edge18, edge15, edge20, edge22, edge21, M_1, edge17, edge23, edge19, edge24, N_1, O_1, P_1, face7, face9, face8, face10
  21. Line(A, yAxis) → f
  22. Line(I, yAxis) → g
  23. Line(A_1, yAxis) → h
  24. Line(I_1, yAxis) → i
  25. Line(A, zAxis) → j
  26. Line(I, zAxis) → k
  27. Line(A_1, zAxis) → l
  28. Line(I_1, zAxis) → m
  29. Rotate(a, α, f) → a'
  30. Rotate(a', β, xAxis) → a''
  31. Rotate(a'', γ, j) → a'''
  32. Rotate(b, δ, g) → b'
  33. Rotate(b', ε, xAxis) → b''
  34. Rotate(b'', ζ, k) → b'''
  35. Rotate(c, (-η), yAxis) → c'
  36. Rotate(c', θ, xAxis) → c''
  37. Rotate(c'', ι, zAxis) → c'''
  38. Rotate(d, κ, h) → d'
  39. Rotate(d', λ, xAxis) → d''
  40. Rotate(d'', μ, l) → d'''
  41. Rotate(e, ν, i) → e'
  42. Rotate(e', ξ, xAxis) → e''
  43. Rotate(e'', ο, m) → e'''
  44. Midpoint(A, B) → Q_1
  45. Midpoint(D, C) → R_1
  46. Midpoint(F, A) → S_1
  47. Midpoint(D, G) → T_1
  48. Midpoint(E, F) → U_1
  49. Prism(D, R_1, Q_1, A, H) → n, V_1, edge27, edge30, edge25, edgeAD, edgeDH, edge32, edge31, edge26, edge28, edge33, W_1, edge34, edge29, Z_1, face14, face16, face18, face15, face13, face17
  50. Prism(W_1, F, S_1, V_1) → o, A_2, edge38, edge40, edge37, edge39, edge41, edge43, edge42, B_2, face19, face22, face21, face23, face20, edge36, edge35
  51. Rotate(n, α, f) → n'
  52. Rotate(n', β, xAxis) → n''
  53. Rotate(n'', γ, j) → n'''
  54. Rotate(o, α, f) → o'
  55. Rotate(o', β, xAxis) → o''
  56. Rotate(o'', γ, j) → o'''
  57. Midpoint(N, J) → C_2
  58. Midpoint(O, K) → D_2
  59. Midpoint(M, N) → E_2
  60. Midpoint(P, O) → F_2
  61. Midpoint(I, J) → G_2
  62. Midpoint(L, K) → H_2
  63. Midpoint(M, I) → I_2
  64. Midpoint(I_2, C_2) → J_2
  65. Midpoint(P, L) → K_2
  66. Midpoint(K_2, D_2) → L_2
  67. Prism(G_2, J, K, H_2, J_2) → p, M_2, edge44, edgeJK, edge46, edge48, edge49, edge45, edge47, edge50, edge51, edge53, N_2, edge54, edge52, O_2, face24, face26, face25, face27, face28, face29
  68. Prism(F_2, O_2, N_2, E_2) → q, P_2, edge58, edge55, edge62, edge61, edge56, edge63, edge57, Q_2, face31, face33, face34, face32, face30, edge59, edge60
  69. Rotate(p, δ, g) → p'
  70. Rotate(p', ε, xAxis) → p''
  71. Rotate(q, δ, g) → q'
  72. Midpoint(V, R) → R_2
  73. Midpoint(R, Q) → S_2
  74. Midpoint(U, V) → T_2
  75. Midpoint(T_2, S_2) → U_2
  76. Midpoint(S, W) → V_2
  77. Midpoint(T, S) → W_2
  78. Prism(S_2, R, S, W_2, U_2) → r, Z_2, edge64, edgeRS, edge66, edge69, edge68, edge65, edge67, edge72, edge70, edge73, A_3, edge74, edge71, B_3, face35, face37, face36, face38, face39, face40
  79. Prism(Z_2, A_3, W, U_2) → s, C_3, edge75, edge78, edge82, edge77, edge79, edge83, edge80, D_3, face41, face45, face44, face43, face42, edge81, edge76
  80. Rotate(r, (-η), yAxis) → r'
  81. Rotate(r', θ, xAxis) → r''
  82. Rotate(r'', ι, zAxis) → r'''
  83. Rotate(s, (-η), yAxis) → s'
  84. Rotate(s', θ, xAxis) → s''
  85. Rotate(s'', ι, zAxis) → s'''
  86. Midpoint(A_1, B_1) → E_3
  87. Midpoint(B_1, F_1) → F_3
  88. Midpoint(E_1, A_1) → G_3
  89. Midpoint(G_3, F_3) → H_3
  90. Midpoint(D_1, A_1) → I_3
  91. Midpoint(C_1, B_1) → J_3
  92. Midpoint(J_3, I_3) → K_3
  93. Prism(A_1, I_3, J_3, B_1, G_3) → t, L_3, edge86, edge91, edge87, edge84, edge85, edge92, edge93, edge88, edge89, edge94, M_3, edge95, edge90, N_3, face46, face48, face51, face49, face47, face50
  94. Midpoint(L_3, M_3) → O_3
  95. Midpoint(F_1, G_1) → P_3
  96. Prism(O_3, P_3, M_3, H_3) → u, Q_3, edge99, edge96, edge103, edge101, edge97, edge104, edge98, R_3, face53, face55, face56, face54, face52, edge102, edge100
  97. Rotate(t, κ, h) → t'
  98. Rotate(t', λ, xAxis) → t''
  99. Rotate(t'', μ, l) → t'''
  100. Rotate(u, κ, h) → u'
  101. Rotate(u', λ, xAxis) → u''
  102. Rotate(u'', μ, l) → u'''
  103. Midpoint(P_1, O_1) → S_3
  104. Midpoint(M_1, N_1) → T_3
  105. Midpoint(L_1, K_1) → U_3
  106. Midpoint(I_1, J_1) → V_3
  107. Midpoint(P_1, M_1) → W_3
  108. Midpoint(O_1, N_1) → Z_3
  109. Midpoint(Z_3, W_3) → A_4
  110. Midpoint(L_1, I_1) → B_4
  111. Midpoint(K_1, J_1) → C_4
  112. Midpoint(C_4, B_4) → D_4
  113. Prism(L_1, B_4, D_4, U_3, P_1) → v, E_4, edge107, edge112, edge110, edge106, edge105, edge113, edge114, edge111, edge108, edge115, F_4, edge116, edge109, G_4, face59, face57, face62, face61, face58, face60
  114. Midpoint(F_4, D_4) → H_4
  115. Midpoint(G_4, U_3) → I_4
  116. Prism(U_3, K_1, I_4, D_4) → w, J_4, edge121, edge120, edge119, edge124, edge122, edge125, edge123, K_4, face63, face65, face66, face67, face64, edge117, edge118
  117. Rotate(v, ν, i) → v'
  118. Rotate(w, ν, i) → w'
  119. Rotate(v', ξ, xAxis) → v''
  120. Rotate(w', ξ, xAxis) → w''
  121. Rotate(v'', ο, m) → v'''
  122. Rotate(w'', ο, m) → w'''
  123. Point(k) → L_4
  124. Point(b''') → Q_4
  125. Point(b''') → R_4
  126. Point(b''') → S_4
  127. Point(b''') → T_4
  128. Prism(H_2, L_2, K_2, M_4, G_2) → a_1, N_4, edge129, edge131, edge132, edge130, edge126, edge134, edge133, edge135, edge127, edge136, O_4, edge137, edge128, P_4, face71, face68, face72, face73, face69, face70
  129. Rotate(a_1, δ, g) → b_1
  130. Rotate(b_1, ε, xAxis) → c_1
  131. Rotate(c_1, ζ, k) → d_1
  132. Prism(U_4, K_2, L_2, L_4) → e_1, V_4, edge141, edge143, edge140, edge142, edge144, edge146, edge145, W_4, face74, face77, face76, face78, face75, edge139, edge138
  133. Rotate(e_1, δ, g) → f_1
  134. Rotate(f_1, ε, xAxis) → g_1
  135. Rotate(g_1, ζ, k) → h_1

AI 绘图提示语参考

画一个立方体，再画另一个立方体，然后分别将它们绕Y轴、X轴和Z轴旋转不同的角度，展示旋转后的立方体。在立方体之间画三条直线，分别平行于X轴、Y轴和Z轴，并标出它们的交点。最后，计算并标出立方体各边的中点，展示这些中点与立方体的关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。