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立方体的两个部分

立方体的两个部分
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2019-04-30 04:41
向量立体几何几何作图
所属专题 TWO PARTS OF A CUBE
这个范例展示了立方体的两个部分。它涉及立方体、割线、二次函数等核心数学概念。通过使用GeoGebra命令如点、立方体、中点、线、向量、平移、旋转等，可以构造立方体的各个面和边。适合初中或高中学生学习立体几何。

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) → c, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Point(xAxis) → L
  6. Point(xAxis) → M
  7. Point(Circle[M, Distance[L, M], Segment[L, M]]) → N
  8. Cube(L, M, N) → k, O, faceNOSR, facePQRS, edgeLO, edgeLM, edgeMN, edgeNO, edgeLP, edgeOS, edgePS, edgePQ, P, edgeMQ, edgeQR, edgeNR, edgeRS, Q, R, S, faceLMNO, faceLOSP, faceLMQP, faceMNRQ
  9. Midpoint(H, B) → S_2
  10. Midpoint(S, M) → S_1
  11. Line(S_1, S_2) → p_1
  12. Line(S_2, yAxis) → f
  13. Line(S_1, yAxis) → g
  14. Line(S_2, zAxis) → h
  15. Line(S_1, zAxis) → i
  16. Point(p_1) → I
  17. Point(p_1) → J
  18. Vector(I, J) → u
  19. Translate(i, Vector[(p * u)]) → i'
  20. Translate(g, Vector[(p * u)]) → g'
  21. Rotate(A, α, p_1) → A'
  22. Rotate(B, α, p_1) → B'
  23. Rotate(C, α, p_1) → C'
  24. Rotate(D, α, p_1) → D'
  25. Rotate(E, α, p_1) → E'
  26. Rotate(F, α, p_1) → F'
  27. Rotate(G, α, p_1) → G'
  28. Rotate(H, α, p_1) → H'
  29. Rotate(A', β, f) → A''
  30. Rotate(B', β, f) → B''
  31. Rotate(C', β, f) → C''
  32. Rotate(D', β, f) → D''
  33. Rotate(E', β, f) → E''
  34. Rotate(F', β, f) → F''
  35. Rotate(G', β, f) → G''
  36. Rotate(H', β, f) → H''
  37. Translate(k, Vector[(p * u)]) → k'
  38. Translate(L, Vector[(p * u)]) → L'
  39. Translate(M, Vector[(p * u)]) → M'
  40. Translate(N, Vector[(p * u)]) → N'
  41. Translate(O, Vector[(p * u)]) → O'
  42. Translate(P, Vector[(p * u)]) → P'
  43. Translate(Q, Vector[(p * u)]) → Q'
  44. Translate(R, Vector[(p * u)]) → R'
  45. Translate(S, Vector[(p * u)]) → S'
  46. Rotate(c, α, p_1) → c'
  47. Rotate(c', β, f) → c''
  48. Rotate(G'', γ, h) → G'''
  49. Rotate(H'', γ, h) → H'''
  50. Rotate(E'', γ, h) → E'''
  51. Rotate(F'', γ, h) → F'''
  52. Rotate(D'', γ, h) → D'''
  53. Rotate(C'', γ, h) → C'''
  54. Rotate(A'', γ, h) → A'''
  55. Rotate(B'', γ, h) → B'''
  56. Rotate(c'', γ, h) → c'''
  57. Rotate(k', δ, p_1) → k''
  58. Rotate(L', δ, p_1) → L''
  59. Rotate(M', δ, p_1) → M''
  60. Rotate(N', δ, p_1) → N''
  61. Rotate(O', δ, p_1) → O''
  62. Rotate(P', δ, p_1) → P''
  63. Rotate(Q', δ, p_1) → Q''
  64. Rotate(R', δ, p_1) → R''
  65. Rotate(S', δ, p_1) → S''
  66. Rotate(k'', ε, g') → k'''
  67. Rotate(L'', ε, g') → L'''
  68. Rotate(M'', ε, g') → M'''
  69. Rotate(N'', ε, g') → N'''
  70. Rotate(O'', ε, g') → O'''
  71. Rotate(P'', ε, g') → P'''
  72. Rotate(Q'', ε, g') → Q'''
  73. Rotate(R'', ε, g') → R'''
  74. Rotate(S'', ε, g') → S'''
  75. Rotate(k''', ζ, i') → a
  76. Rotate(L''', ζ, i') → K
  77. Rotate(M''', ζ, i') → T
  78. Rotate(N''', ζ, i') → U
  79. Rotate(O''', ζ, i') → V
  80. Rotate(P''', ζ, i') → W
  81. Rotate(Q''', ζ, i') → Z
  82. Rotate(R''', ζ, i') → A_1
  83. Rotate(S''', ζ, i') → B_1
  84. Midpoint(H''', G''') → C_1
  85. Midpoint(E''', F''') → D_1
  86. Midpoint(D''', C''') → E_1
  87. Midpoint(A''', B''') → F_1
  88. Midpoint(A''', D''') → G_1
  89. Midpoint(E''', H''') → H_1
  90. Midpoint(F''', G''') → I_1
  91. Midpoint(B''', C''') → J_1
  92. Midpoint(C_1, D_1) → K_1
  93. Midpoint(C_1, E_1) → L_1
  94. Midpoint(G_1, H_1) → M_1
  95. Midpoint(D_1, F_1) → N_1
  96. Midpoint(J_1, I_1) → O_1
  97. Midpoint(G_1, J_1) → P_1
  98. Midpoint(V, T) → Q_1
  99. Midpoint(B_1, Z) → R_1
  100. Midpoint(A_1, T) → T_1
  101. Midpoint(B_1, U) → U_1
  102. Midpoint(B_1, K) → V_1
  103. Midpoint(Z, K) → W_1
  104. Midpoint(B_1, A_1) → Z_1
  105. Midpoint(A_1, Z) → A_2
  106. Midpoint(Z, W) → B_2
  107. Midpoint(V, U) → C_2
  108. Midpoint(K, T) → D_2
  109. Midpoint(T, U) → E_2
  110. Midpoint(V, K) → F_2
  111. Midpoint(B_1, W) → G_2
  112. Midpoint(Z, T) → H_2
  113. Midpoint(K, W) → I_2
  114. Midpoint(B_1, V) → J_2
  115. Midpoint(U, A_1) → K_2
  116. Midpoint(G''', C''') → L_2
  117. Midpoint(D''', H''') → M_2
  118. Midpoint(A''', E''') → N_2
  119. Midpoint(F''', B''') → O_2
  120. Prism(H''', C_1, L_2, C''', E_1, M_2, H_1) → b, P_2, face3, face6, face2, face8, edge1, edge7, edge5, edge4, edge9, edge3, Q_2, edge2, edge8, edge13, edge6, edge10, edge14, edge11, edge15, edge16, edge17, R_2, edge18, edge12, T_2, U_2, face7, face1, face5, face4
  121. Prism(P_2, U_2, H_1, D_1) → d, V_2, edge22, edge19, edge26, edge24, edge20, edge27, edge21, W_2, face10, face12, face13, face11, face9, edge25, edge23
  122. Prism(Q_2, R_2, T_2, O_2) → e, Z_2, edge32, edge28, edge34, edge35, edge29, edge36, edge30, A_3, face15, face16, face18, face17, face14, edge31, edge33
  123. Prism(U, V, F_2, D_2, T, K_2) → j, B_3, face19, face25, edgeUV, edge40, edge42, edge37, edgeTU_1, edge39, edge41, edge44, C_3, edge43, edge38, edge45, edge47, edge48, edge49, edge46, D_3, E_3, face24, face21, face22, face23, face20
  124. Prism(K_2, T_1, U_1, A_1) → l, F_3, edge56, edge50, edge55, edge57, edge51, edge58, edge52, G_3, face27, face28, face30, face29, face26, edge54, edge53
  125. Prism(Z, T, U, A_1, B_2) → n, H_3, edgeTZ, edgeTU, edge60, edge62, edge63, edge59, edge61, edge64, edge65, edge67, I_3, edge68, edge66, J_3, face31, face33, face32, face34, face35, face36
  126. Prism(U_1, I_3, Q_1, J_2) → o, K_3, edge69, edge72, edge76, edge71, edge74, edge77, edge75, L_3, face37, face41, face40, face39, face38, edge73, edge70
  127. Prism(R_1, W_1, B_2, G_2) → q, M_3, edge79, edge80, edge82, edge83, edge84, edge86, edge85, N_3, face42, face44, face46, face45, face43, edge78, edge81
  128. Prism(A_2, A_1, K_2, E_2, T, H_2, R_1) → s, O_3, face47, face48, face51, face54, edge90, edge91, edge97, edge87, edge88, edge96, P_3, edge93, edge92, edge100, edge98, edge89, edge99, edge94, edge101, edge102, edge103, Q_3, edge104, edge95, R_3, S_3, face53, face49, face50, face52
  129. Prism(S_3, R_3, Q_3, I_2) → t, T_3, edge109, edge105, edge112, edge110, edge106, edge113, edge107, U_3, face56, face58, face59, face57, face55, edge111, edge108
  130. Prism(R_1, P_3, O_3, G_2) → v, V_3, edge115, edge114, edge121, edge120, edge117, edge122, edge118, W_3, face60, face62, face64, face63, face61, edge116, edge119
  131. Prism(F_2, C_2, U, E_2, D_2, K, V_1) → a_1, Z_3, face70, face65, face66, face72, edge132, edge126, edge127, edge134, edge123, edge124, A_4, edge129, edge133, edge128, edge136, edge135, edge125, edge130, edge137, edge138, edge139, B_4, edge140, edge131, C_4, D_4, face71, face69, face67, face68
  132. Prism(V_1, Z_3, J_2, G_2) → b_1, E_4, edge142, edge141, edge148, edge147, edge144, edge149, edge145, F_4, face73, face75, face77, face76, face74, edge143, edge146
  133. Prism(B_4, H_2, C_4, A_2) → c_1, G_4, edge156, edge150, edge155, edge157, edge151, edge158, edge152, H_4, face79, face80, face82, face81, face78, edge153, edge154

AI 绘图提示语参考

绘制一个立方体的两个部分，分别以点A、B和C以及点L、M和N为顶点。通过点A、B和C构造一个立方体，然后通过点L、M和N构造另一个立方体。接着，找到H和B的中点S₂，以及S和M的中点S₁，连接S₁和S₂得到直线p₁，再从S₂出发沿y轴方向画直线f，从S₁出发沿z轴方向画直线g，从S₂出发沿z轴方向画直线h，从S₁出发沿z轴方向画直线i。然后在直线p₁上取两点I和J，连接I和J得到向量u，将直线i、g、h、i沿向量u平移，将点A、B、C、D、E、F、G、H绕直线p₁旋转α度，再将点A、B、C、D、E、F、G、H绕直线f旋转β度，最后将立方体c绕直线p₁旋转α度，再绕直线f旋转β度，最后将点G绕直线h旋转γ度。
以上提示语为根据原始绘图命令整理而来，仅供参考。