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立方体的两部分 by Renáta Vágová

立方体的两部分 by Renáta Vágová
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2019-04-30 00:57
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部分。它涉及立体几何中的基本概念，如点、线、面和多面体。通过使用GeoGebra命令如点、立方体、中点、线、向量、平移和旋转，可以构造出立方体的两个部分。适合初中及以上学生学习立体几何。

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(D''', B''') → C_1
  85. Midpoint(D''', A''') → D_1
  86. Midpoint(A''', B''') → E_1
  87. Midpoint(D''', C''') → F_1
  88. Midpoint(C''', B''') → G_1
  89. Pyramid(D_1, C_1, F_1, D''', H''') → b, face5, edge2, edge1, edge3, edgeD'''H''', face3, face4, face2, face1, edge6, edge7, edge5, edge4
  90. Pyramid(C''', F_1, C_1, G_1, G''') → d, face10, edgeC'''G''', edge9, edge8, edge10, face6, face8, face9, face7, edge11, edge13, edge14, edge12
  91. Pyramid(D_1, C_1, E_1, A''', E''') → e, face15, edge16, edge15, edge17, edgeA'''E''', face13, face14, face12, face11, edge20, edge21, edge19, edge18
  92. Pyramid(C_1, E_1, B''', G_1, F''') → j, face20, edge22, edge23, edgeB'''F''', edge24, face18, face16, face17, face19, edge27, edge25, edge26, edge28
  93. Midpoint(B_1, A_1) → H_1
  94. Midpoint(A_1, U) → I_1
  95. Midpoint(U, V) → J_1
  96. Midpoint(V, B_1) → K_1
  97. Midpoint(B_1, W) → L_1
  98. Midpoint(W, K) → M_1
  99. Midpoint(K, T) → N_1
  100. Midpoint(T, U) → O_1
  101. Midpoint(Z, T) → P_1
  102. Midpoint(Z, A_1) → Q_1
  103. Midpoint(M_1, P_1) → R_1
  104. Midpoint(H_1, J_1) → T_1
  105. Midpoint(Q_1, O_1) → U_1
  106. Midpoint(K, V) → V_1
  107. Midpoint(V_1, L_1) → W_1
  108. Prism(K_1, A_1, U, M_1) → l, Z_1, edge30, edge34, edge33, edge31, edge35, edge37, edge36, A_2, face21, face25, face23, face24, face22, edge32, edge29
  109. Prism(Z_1, A_1, L_1, A_2) → m, B_2, edge41, edge43, edge40, edge42, edge44, edge46, edge45, C_2, face26, face29, face28, face30, face27, edge39, edge38
  110. Midpoint(V, T) → D_2
  111. Pyramid(B_1, W, Z, A_1, D_2) → o, face35, edge53, edge48, edge50, edge52, face32, face31, face33, face34, edge47, edgeWZ_1, edge49, edge51
  112. Pyramid(V_1, K, T, O_1, Z) → r, face39, edge57, edgeKZ, edgeTZ, edge56, face36, faceKTZ, face37, face38, edge54, edgeKT_1, edge55, edge58
  113. Pyramid(O_1, T, K, V_1, W) → s, face43, edge61, edgeTW, edgeKW, edge62, face41, faceKTW, face40, face42, edge60, edgeKT, edge59, edge63
  114. Pyramid(V_1, V, U, O_1, B_1) → t, face48, edge69, edge66, edge64, edge68, face46, face44, face45, face47, edge67, edgeUV_1, edge65, edge70
  115. Pyramid(V_1, V, U, O_1, A_1) → v, face53, edge76, edge73, edge71, edge75, face51, face49, face50, face52, edge74, edgeUV, edge72, edge77
  116. Pyramid(B_1, A_1, J_1, D_2) → a_1, face54, edge83, face55, face56, face57, edge78, edge79, edge81, edge82, edge80
  117. Pyramid(W, B_1, V_1, D_2) → b_1, face58, edge89, face59, face61, face60, edge84, edge87, edge85, edge86, edge88
  118. Pyramid(W, Z, N_1, D_2) → c_1, face62, edge94, face63, face65, face64, edgeWZ, edge92, edge90, edge91, edge93
  119. Pyramid(A_1, Z, O_1, D_2) → d_1, face66, edge100, face67, face68, face69, edge95, edge96, edge98, edge99, edge97