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立方体部分演示 by Renáta Vágová (2)

立方体部分演示 by Renáta Vágová (2)
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2019-04-30 02:24
向量解析几何立体几何微积分几何作图
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、向量运算、几何变换和积分计算；③构造过程中使用了Point, Cube, Midpoint, Line, Vector, Translate, Rotate, Prism等GeoGebra命令和对象；④适合高中及以上学生用于学习立体几何和空间向量，也可用于大学基础数学教学。

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''', A''') → C_1
  85. Midpoint(A''', B''') → D_1
  86. Midpoint(B''', C''') → E_1
  87. Midpoint(C''', D''') → F_1
  88. Midpoint(H''', E''') → G_1
  89. Midpoint(H''', F''') → H_1
  90. Midpoint(H''', G''') → I_1
  91. Midpoint(F_1, D_1) → J_1
  92. Midpoint(C_1, G_1) → K_1
  93. Midpoint(G''', F''') → L_1
  94. Midpoint(L_1, E_1) → M_1
  95. Midpoint(H''', D''') → N_1
  96. Midpoint(F''', B''') → O_1
  97. Midpoint(O_1, N_1) → P_1
  98. Prism(C_1, J_1, F_1, D''', G_1) → b, Q_1, edge5, edge6, edge2, edge1, edge4, edge10, edge7, edge3, edge8, edge11, R_1, edge12, edge9, T_1, face2, face4, face5, face3, face1, face6
  99. Prism(C_1, K_1, A''', J_1) → d, U_1, edge13, edge16, edge20, edge15, edge18, edge21, edge19, V_1, face7, face11, face10, face9, face8, edge17, edge14
  100. Midpoint(R_1, F_1) → W_1
  101. Prism(W_1, F_1, C''', U_1) → e, Z_1, edge23, edge27, edge26, edge24, edge28, edge30, edge29, A_2, face12, face16, face14, face15, face13, edge25, edge22
  102. Midpoint(B_1, A_1) → B_2
  103. Midpoint(A_1, Z) → C_2
  104. Midpoint(B_1, W) → D_2
  105. Midpoint(W, Z) → E_2
  106. Midpoint(B_1, V) → F_2
  107. Midpoint(V, U) → G_2
  108. Midpoint(U, A_1) → H_2
  109. Midpoint(B_2, G_2) → I_2
  110. Midpoint(K, T) → J_2
  111. Midpoint(T, Z) → K_2
  112. Midpoint(W, K) → L_2
  113. Midpoint(K_2, L_2) → M_2
  114. Midpoint(F_2, L_2) → N_2
  115. Midpoint(H_2, K_2) → O_2
  116. Midpoint(J_2, G_2) → P_2
  117. Midpoint(B_2, E_2) → Q_2
  118. Midpoint(Q_2, P_2) → R_2
  119. Prism(B_1, B_2, I_2, V, W) → j, T_2, edge37, edge38, edge32, edge31, edge34, edge39, edge40, edge33, edge35, edge41, U_2, edge42, edge36, V_2, face18, face20, face22, face19, face17, face21
  120. Prism(C_2, A_1, U, O_2, Q_2) → l, W_2, edge46, edge43, edge44, edge48, edge49, edge47, edge45, edge50, edge51, edge53, Z_2, edge54, edge52, A_3, face23, face26, face24, face25, face27, face28
  121. Midpoint(U, T) → B_3
  122. Midpoint(V, K) → C_3
  123. Prism(D_2, C_2, B_3, P_2, R_2, W) → n, D_3, face30, face34, edge58, edge59, edge63, edge62, edge61, edge55, edge60, edge66, E_3, edge64, edge65, edge56, edge67, edge68, edge69, edge57, F_3, G_3, face35, face29, face31, face33, face32
  124. Prism(A_1, C_2, O_2, B_2) → o, H_3, edge72, edge70, edge76, edge77, edge73, edge78, edge74, I_3, face36, face38, face40, face39, face37, edge71, edge75
  125. Prism(C_3, N_2, W, K, P_2) → r, J_3, edge83, edge81, edgeKW, edge79, edge85, edge84, edge82, edge80, edge86, edge88, K_3, edge89, edge87, L_3, face41, face45, face44, face42, face43, face46
  126. Prism(Q_2, K_3, Z, C_2, P_2) → s, M_3, edge98, edge91, edge90, edge93, edge95, edge99, edge92, edge94, edge96, edge100, N_3, edge101, edge97, O_3, face47, face51, face49, face48, face50, face52
  127. Prism(P_2, J_3, C_2, O_3, G_2) → t, P_3, edge108, edge102, edge103, edge109, edge105, edge110, edge104, edge111, edge106, edge112, Q_3, edge113, edge107, R_3, face53, face56, face54, face55, face57, face58
  128. Prism(V, N_2, D_2, B_1, U) → w, S_3, edge117, edge120, edge118, edge116, edgeUV, edge122, edge121, edge119, edge114, edge123, T_3, edge124, edge115, U_3, face62, face60, face64, face63, face59, face61
  129. Prism(S_3, U, T, K_2, R_2) → a_1, V_3, edge127, edgeTU, edge125, edge129, edge131, edge128, edge126, edge130, edge132, edge134, W_3, edge135, edge133, Z_3, face65, face68, face66, face67, face69, face70
  130. Prism(Z_3, R_2, S_3, K_2, E_2) → b_1, A_4, edge143, edge142, edge139, edge140, edge136, edge144, edge145, edge141, edge137, edge146, B_4, edge147, edge138, C_4, face74, face72, face76, face75, face71, face73