积极 AI Logo 积极 AI

立方体部分演示 by Renáta Vágová

立方体部分演示 by Renáta Vágová
几何画板及绘图内容加载中，请稍等……
2019-04-30 07:10
向量解析几何立体几何变换几何作图
所属专题 TWO PARTS OF A CUBE
①本范例演示立方体的两个部分及其几何关系；②涉及核心数学概念包括立体几何、向量、中点、旋转和平移；③构造要点：使用 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学习和理解空间几何与变换。

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. Midpoint(M_2, D''') → P_2
  121. Midpoint(N_2, A''') → Q_2
  122. Midpoint(L_2, C''') → R_2
  123. Midpoint(O_2, B''') → T_2
  124. Midpoint(O_1, M_1) → U_2
  125. Midpoint(U_2, P_1) → V_2
  126. Prism(P_2, Q_2, T_2, V_2, R_2, H''') → b, W_2, face2, face6, edge4, edge6, edge10, edge8, edge5, edge1, edge7, edge11, Z_2, edge12, edge9, edge2, edge13, edge14, edge15, edge3, A_3, B_3, face7, face1, face3, face5, face4
  127. Prism(B_1, V_1, V, A_1) → d, C_3, edge16, edge19, edge23, edge18, edge20, edge24, edge21, D_3, face8, face12, face11, face10, face9, edge22, edge17
  128. Midpoint(B_2, W) → E_3
  129. Midpoint(D_2, K) → F_3
  130. Midpoint(G_2, R_1) → G_3
  131. Midpoint(Q_1, F_2) → H_3
  132. Prism(W, G_2, V_1, V, K, E_3) → e, I_3, face14, face19, edge28, edge30, edge26, edgeKV_1, edgeKW_1, edge29, edge32, edge31, J_3, edge27, edge25, edge33, edge35, edge36, edge37, edge34, K_3, L_3, face18, face16, face17, face15, face13
  133. Midpoint(B_2, Z) → M_3
  134. Midpoint(Z_1, A_1) → N_3
  135. Midpoint(D_2, T) → O_3
  136. Midpoint(C_2, U) → P_3
  137. Midpoint(V_1, T_1) → Q_3
  138. Midpoint(Q_3, T_1) → R_3
  139. Prism(V, K, V_1, U) → l, S_3, edge42, edgeUV_1, edge39, edge43, edge40, edge44, edge41, T_3, face20, face22, face23, face24, face21, edgeKV_2, edge38
  140. Midpoint(B_1, Z_1) → U_3
  141. Prism(B_1, V, V_1, K, W, U_3) → m, V_3, face29, face31, edge47, edge48, edge45, edgeKW, edge50, edge52, edge49, edge53, W_3, edge46, edge51, edge54, edge56, edge57, edge58, edge55, Z_3, A_4, face30, face27, face28, face26, face25
  142. Midpoint(N_3, P_3) → B_4
  143. Midpoint(B_4, P_3) → C_4
  144. Midpoint(K_2, U) → D_4
  145. Midpoint(H_2, T) → E_4
  146. Prism(U, T, E_4, D_4, V) → o, F_4, edgeTU, edge59, edge64, edge61, edgeUV_2, edge60, edge66, edge65, edge62, edge67, G_4, edge68, edge63, H_4, face33, face32, face34, face37, face35, face36
  147. Prism(A_1, N_3, R_1, M_3, Z, D_4) → q, I_4, face38, face44, edge72, edge75, edge74, edge70, edge69, edge73, edge78, edge76, J_4, edge77, edge71, edge79, edge81, edge82, edge83, edge80, K_4, L_4, face43, face40, face42, face41, face39
  148. Prism(V, K, E_2, B_1) → s, M_4, edge87, edge86, edge85, edge90, edge88, edge91, edge89, N_4, face45, face47, face48, face49, face46, edgeKV, edge84
  149. Prism(U, E_2, V, D_4) → t, O_4, edgeUV, edge93, edge96, edge95, edge97, edge99, edge98, P_4, face50, face53, face54, face52, face51, edge92, edge94
  150. Prism(T, E_2, K, E_4) → v, Q_4, edgeKT, edge103, edge104, edge101, edge105, edge107, edge106, R_4, face55, face59, face58, face57, face56, edge102, edge100