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Two Parts of a Cube by Renáta Vágová (2)

Two Parts of a Cube by Renáta Vágová (2)
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2019-04-29 23:48
Coordinate GeometrySolid GeometryGeometric Construction
In collections TWO PARTS OF A CUBE
This example demonstrates two parts of a cube. It involves core mathematical concepts such as cube, line segment, coordinates, and continuity. Using GeoGebra commands like Point, Cube, Midpoint, Line, Vector, Translate, Rotate, Polygon, Segment, etc., the two parts of the cube can be constructed. Suitable for high school geometry education.

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. 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}