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立方体的两部分 by Renáta Vágová (2)

立方体的两部分 by Renáta Vágová (2)
几何画板及绘图内容加载中，请稍等……
2019-04-29 23:48
解析几何立体几何几何作图
所属专题 TWO PARTS OF A CUBE
这个范例展示了立方体的两部分。它涉及立方体、线段、坐标和连续性等核心数学概念。通过使用GeoGebra命令如点、立方体、中点、线、向量、平移、旋转、多边形、线段等，可以构造出立方体的两部分。适合用于高中几何教学。

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. Polygon(L_1, C''', G''', F_1) → q1, l_1, m, g''', f_1
  85. Polygon(L_1, C_1, B''', C''') → q2, n, c_1, b''', r
  86. Polygon(C''', K_1, G_1, G''') → q3, s, k_1, g_1, t
  87. Midpoint(M_1, G_1) → N_1
  88. Polygon(L_1, J_1, N_1, F_1) → q4, b, j_1, n_1, d
  89. Polygon(N_1, G_1, G''', F_1) → q5, h_1, i_1, m_1, q_1
  90. Polygon(I_1, E_1, G_1, N_1) → q6, r_1, e_1, s_1, t_1
  91. Polygon(I_1, J_1, C_1) → t1, a_1, b_1, d_1
  92. Polygon(E_1, K_1, B''') → t2, f_2, g_2, h_2
  93. Polygon(C_1, B''', E_1, I_1) → q7, i_2, j_2, k_2, l_2
  94. Segment(N_1, I_1) → m_2
  95. Segment(G_1, E_1) → n_2
  96. Polygon(K, V, W_1, A_2, V_1, T) → poly1, k_3, v, w_1, a_2, v_1, t_2
  97. Polygon(V, D_2, C_2, W_1) → q8, v_2, d_2, c_2, j
  98. Polygon(C_2, A_2, W_1) → t3, l, q, e
  99. Polygon(V, D_2, R_1, W, K) → poly2, v_3, p_2, q_2, w, k_4
  100. Polygon(R_1, B_2, C_2, D_2) → q9, r_2, b_2, s_2, e_2
  101. Polygon(R_1, T_1, Z, W) → q10, f_3, g_3, z_1, w_2
  102. Polygon(A_2, V_1, T_1, B_2) → q11, h_3, i_3, j_3, l_3
  103. Polygon(T, V_1, T_1, Z) → q12, t_3, m_3, n_3, z_2
  104. Polygon(T, K, W, Z) → q13, t_4, k_5, w_3, z_3
  105. Polygon(V, U, A_1, B_1) → q14, v_4, u_1, p_3, q_3
  106. Polygon(U, V_1, T_1, A_1) → q15, u_2, r_3, s_3, a_3
  107. Polygon(J_2, B_2, T_1, A_1, B_1, W) → poly3, b_3, c_3, d_3, e_3, f_4, w_4
  108. Polygon(V, K, W, B_1) → q16, v_5, k_6, w_5, g_4
  109. Polygon(W, K, T, K_2, J_2) → poly4, w_6, k_7, t_5, h_4, i_4
  110. Polygon(K_2, C_2, V_1, T) → q17, j_4, l_4, m_4, t_6
  111. Point(j_4) → P_1
  112. Polygon(K_2, C_2, B_2, J_2) → q18, n_4, p_4, q_4, r_4
  113. Polygon(B_2, C_2, V_1, T_1) → q19, s_4, a_4, b_4, c_4
  114. Midpoint(B_1, V) → O_1
  115. Midpoint(B_1, A_1) → Q_1
  116. Midpoint(Z, T) → E_2
  117. Midpoint(U, A_1) → F_2
  118. Midpoint(F_2, E_2) → G_2
  119. Polygon(O_1, F_2, A_1, B_1) → q20, d_4, e_4, f_5, g_5
  120. Midpoint(W, K) → H_2
  121. Polygon(O_1, D_2, H_2, C_2, G_2, F_2) → poly5, h_5, i_5, j_5, l_5, m_5, n_5
  122. Polygon(H_2, K, A_2, C_2) → q21, p_5, k_8, q_5, r_5
  123. Polygon(A_2, V_1, G_2, C_2) → q22, s_5, a_5, b_5, c_5
  124. Polygon(O_1, H_2, W, B_1) → q23, d_5, e_5, w_7, f_6
  125. Polygon(W, Z, A_1, B_1) → q24, w_8, z_4, g_6, h_6
  126. Polygon(K, T, Z, W) → q25, k_9, t_7, z_5, w_9
  127. Polygon(V, U, A_1, B_1) → q27, v_6, u_4, j_6, l_6
  128. Polygon(V, U_1, R_1, B_1) → q28, v_7, m_6, n_6, p_6
  129. Polygon(B_1, A_1, T_1, R_1) → q29, q_6, r_6, s_6, a_6
  130. Polygon(A_1, U, T, E_2, G_2, T_1) → poly6, b_6, u_5, t_9, c_6, d_6, e_6
  131. Polygon(C_2, A_2, T, E_2) → q30, f_7, g_7, t_{10}, h_7
  132. Polygon(U_1, A_2, C_2, G_2, T_1, R_1) → poly7, i_7, j_7, l_7, m_7, n_7, p_7
  133. Polygon(C_2, E_2, G_2) → t4, q_7, r_7, s_7
  134. Midpoint(K, V) → I_2
  135. Midpoint(T, V) → L_2
  136. Polygon(I_2, V, U, T, L_2) → poly8, a_7, v_8, u_6, t_{11}, b_7
  137. Midpoint(Z, U) → M_2
  138. Midpoint(U, A_1) → N_2
  139. Midpoint(T, U) → O_2
  140. Polygon(T, O_2, M_2, N_2, A_1, Z) → poly9, t_8, i_6, c_7, d_7, e_7, z_6
  141. Polygon(K, L_2, O_2, T) → q26, k_{10}, f_8, g_8, t_{12}
  142. Polygon(K, V, U, T) → q31, k_{11}, v_9, u_3, t_{13}