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立方体部分演示 by Renáta Vágová (4)

立方体部分演示 by Renáta Vágová (4)
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2019-04-27 16:51
向量立体几何几何作图
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、直线、三角形面积、函数和变换；③构造过程中用到了点、立方体、中点、线、向量、平移、旋转、多边形等GeoGebra命令；④适合高中及以上学生学习和理解空间几何与向量知识。

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. Polygon(D''', C''', G''', C_1, M_2) → poly1, d''', j, g''', c_1, m_2
  121. Polygon(D''', G_1, F_1, B''', C''') → poly2, l, g_1, f_1, b''', m
  122. Polygon(G''', C''', B''', O_2, I_1) → poly3, n, q, r, o_2, i_1
  123. Polygon(C_1, G''', I_1) → t1, s, t, b
  124. Polygon(M_2, D''', G_1) → t2, d, e, h_1
  125. Polygon(F_1, B''', O_2) → t3, j_1, k_1, l_1
  126. Polygon(M_2, G_1, F_1, O_2, I_1, C_1) → poly4, m_1, n_1, q_1, r_1, s_1, t_1
  127. Polygon(B_1, V, Z_1) → t4, z_1, b_1, v
  128. Polygon(B_1, V, K, W) → q1, a_1, v_1, k_2, w
  129. Polygon(K, D_2, V) → t5, v_2, k_3, d_2
  130. Polygon(D_2, H_2, V) → t6, v_3, d_1, h_2
  131. Polygon(Z_1, V, H_2) → t7, e_1, f_2, v_4
  132. Polygon(K, D_2, H_2, Z, W) → poly5, k_4, g_2, i_2, z_2, w_1
  133. Polygon(W, B_1, Z_1, Z) → q2, w_2, j_2, l_2, z_3
  134. Polygon(Z, H_2, Z_1) → t8, n_2, z_4, p_2
  135. Polygon(B_1, U, V) → t9, v_5, q_2, u_1
  136. Polygon(B_1, V, K, W) → q3, r_2, v_6, k_5, w_3
  137. Polygon(U, V, K, T) → q4, u_2, v_7, k_6, t_2
  138. Polygon(U, H_2, T) → t10, t_3, u_3, s_2
  139. Polygon(B_1, U, H_2, B_2) → q5, a_2, u_4, b_2, c_2
  140. Polygon(B_1, W, B_2) → t11, e_2, f_3, w_4
  141. Polygon(W, K, T, H_2, B_2) → poly6, w_5, k_7, t_4, g_3, h_3
  142. Polygon(V, C_2, E_2, T, K) → poly7, v_8, i_3, j_3, t_5, k_8
  143. Polygon(J_2, C_2, V) → t12, v_9, l_3, m_3
  144. Polygon(K, V, J_2, G_2, W) → poly8, k_9, v_{10}, n_3, p_3, w_6
  145. Polygon(T, K, W, B_2, H_2) → poly9, t_6, k_{10}, w_7, q_3, r_3
  146. Polygon(H_2, T, E_2) → t13, s_3, a_3, t_7
  147. Polygon(B_2, G_2, W) → t14, w_8, b_3, c_3
  148. Polygon(E_2, C_2, J_2, G_2, B_2, H_2) → poly10, d_3, e_3, f_4, g_4, h_4, i_4
  149. Polygon(T, V, K) → t15, k_{11}, t_8, v_{11}
  150. Polygon(K, W, Z, T) → q6, k_{12}, w_9, z_5, t_9
  151. Polygon(W, Z, B_1) → t16, j_4, w_{10}, z_6
  152. Polygon(K, W, B_1, V) → q7, k_{13}, w_{11}, l_4, v_{12}
  153. Polygon(B_1, Z, T, V) → q8, m_4, z_7, t_{10}, v_{13}