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Cube Parts Demonstration by Renáta Vágová

Cube Parts Demonstration by Renáta Vágová
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2019-04-30 07:10
VectorCoordinate GeometrySolid GeometryTransformationGeometric Construction
In collections TWO PARTS OF A CUBE
This example demonstrates two parts of a cube and their geometric relationships. It involves core math concepts like solid geometry, vectors, midpoints, rotations, and translations. Construction highlights include using commands and objects such as Point, Cube, Midpoint, Line, Vector, Translate, Rotate, Prism in GeoGebra. Suitable for high school and above students to learn spatial geometry and transformations.

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. 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