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立方体的两部分

立方体的两部分
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2019-04-30 03:52
角立体几何几何作图
所属专题 TWO PARTS OF A CUBE
这个范例展示了立方体的两部分。它涉及的角度、直线、二次函数、对称性等核心数学概念。通过使用GeoGebra命令如Point、Cube、Midpoint、Line等，可以构造立方体的各个面和边。适合用于中学几何教学，帮助学生理解立体几何的基本概念。

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, G''', L_2, C''', E_1, M_2, H_1) → b, P_2, face2, face6, face5, face7, face4, face9, edge4, edge1, edge2, edge8, Q_2, edge7, edge11, edge6, edge5, edge10, edge3, edge15, edge9, edge12, edge16, R_2, edge13, edge17, edge18, edge19, edge20, edge21, edge14, T_2, U_2, V_2, face8, face3, face1
  121. Prism(P_2, Q_2, R_2, D_1) → d, W_2, edge26, edge22, edge28, edge29, edge23, edge30, edge24, Z_2, face11, face12, face14, face13, face10, edge25, edge27
  122. Prism(T, D_2, F_2, V, U, H_2) → e, A_3, face15, face21, edge31, edge36, edge34, edgeUV_1, edgeTU_1, edge32, edge37, edge38, B_3, edge35, edge33, edge39, edge41, edge42, edge43, edge40, C_3, D_3, face20, face16, face19, face18, face17
  123. Midpoint(T_1, B_3) → E_3
  124. Prism(T_1, E_3, U_1, D_3, A_2) → j, F_3, edge46, edge48, edge47, edge45, edge44, edge53, edge49, edge52, edge50, edge54, G_3, edge55, edge51, H_3, face24, face22, face26, face25, face23, face27
  125. Prism(A_1, U, T, Z, Z_1) → m, I_3, edge57, edgeTU_2, edgeTZ, edge59, edge61, edge58, edge56, edge60, edge62, edge64, J_3, edge65, edge63, K_3, face28, face31, face29, face30, face32, face33
  126. Prism(R_1, W_1, K_3, G_2) → n, L_3, edge68, edge67, edge70, edge73, edge71, edge74, edge72, M_3, face34, face36, face38, face37, face35, edge66, edge69
  127. Prism(Z_1, J_2, B_1, R_1) → q, N_3, edge75, edge78, edge82, edge77, edge79, edge83, edge80, O_3, face39, face43, face42, face41, face40, edge81, edge76
  128. Prism(O_3, A_2, T_1, Q_1, F_2, W) → r, P_3, face45, face49, edge92, edge90, edge87, edge88, edge94, edge84, edge93, edge91, Q_3, edge89, edge95, edge85, edge96, edge97, edge98, edge86, R_3, S_3, face50, face44, face48, face46, face47
  129. Prism(U, T, K, V, K_2) → t, T_3, edgeTU, edgeKT, edgeKV, edgeUV, edge101, edge100, edge99, edge102, edge103, edge105, U_3, edge106, edge104, V_3, faceKTUV, face53, face51, face52, face54, face55
  130. Prism(T_1, W_1, T_3, A_2) → v, W_3, edge109, edge108, edge111, edge114, edge112, edge115, edge113, Z_3, face56, face58, face60, face59, face57, edge107, edge110