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Cube Parts Demonstration by Renáta Vágová (4)

Cube Parts Demonstration by Renáta Vágová (4)
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2019-04-27 16:51
VectorSolid GeometryGeometric Construction
In collections TWO PARTS OF A CUBE
This example demonstrates different parts of a cube and their geometric relationships. It involves core mathematical concepts such as solid geometry, vectors, straight lines, area, functions, and transformations. The construction uses commands like Point, Cube, Midpoint, Line, Vector, Translate, Rotate, and Polygon in GeoGebra. It is suitable for high school and above students studying spatial geometry and vector knowledge.

GeoGebra Commands & Parameters

  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}