MathPlotAI Logo MathPlotAI

Cube Parts Demonstration by Renáta Vágová (2)

Cube Parts Demonstration by Renáta Vágová (2)
Loading the math board and drawing, please wait…
2019-04-30 02:24
VectorCoordinate GeometrySolid GeometryCalculusGeometric 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, vector operations, geometric transformations, and definite integrals. The construction uses commands and objects like Point, Cube, Midpoint, Line, Vector, Translate, Rotate, Prism in GeoGebra. It is suitable for high school and university students learning solid geometry and spatial vectors, as well as for introductory mathematics 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. Midpoint(D''', A''') → C_1
  85. Midpoint(A''', B''') → D_1
  86. Midpoint(B''', C''') → E_1
  87. Midpoint(C''', D''') → F_1
  88. Midpoint(H''', E''') → G_1
  89. Midpoint(H''', F''') → H_1
  90. Midpoint(H''', G''') → I_1
  91. Midpoint(F_1, D_1) → J_1
  92. Midpoint(C_1, G_1) → K_1
  93. Midpoint(G''', F''') → L_1
  94. Midpoint(L_1, E_1) → M_1
  95. Midpoint(H''', D''') → N_1
  96. Midpoint(F''', B''') → O_1
  97. Midpoint(O_1, N_1) → P_1
  98. Prism(C_1, J_1, F_1, D''', G_1) → b, Q_1, edge5, edge6, edge2, edge1, edge4, edge10, edge7, edge3, edge8, edge11, R_1, edge12, edge9, T_1, face2, face4, face5, face3, face1, face6
  99. Prism(C_1, K_1, A''', J_1) → d, U_1, edge13, edge16, edge20, edge15, edge18, edge21, edge19, V_1, face7, face11, face10, face9, face8, edge17, edge14
  100. Midpoint(R_1, F_1) → W_1
  101. Prism(W_1, F_1, C''', U_1) → e, Z_1, edge23, edge27, edge26, edge24, edge28, edge30, edge29, A_2, face12, face16, face14, face15, face13, edge25, edge22
  102. Midpoint(B_1, A_1) → B_2
  103. Midpoint(A_1, Z) → C_2
  104. Midpoint(B_1, W) → D_2
  105. Midpoint(W, Z) → E_2
  106. Midpoint(B_1, V) → F_2
  107. Midpoint(V, U) → G_2
  108. Midpoint(U, A_1) → H_2
  109. Midpoint(B_2, G_2) → I_2
  110. Midpoint(K, T) → J_2
  111. Midpoint(T, Z) → K_2
  112. Midpoint(W, K) → L_2
  113. Midpoint(K_2, L_2) → M_2
  114. Midpoint(F_2, L_2) → N_2
  115. Midpoint(H_2, K_2) → O_2
  116. Midpoint(J_2, G_2) → P_2
  117. Midpoint(B_2, E_2) → Q_2
  118. Midpoint(Q_2, P_2) → R_2
  119. Prism(B_1, B_2, I_2, V, W) → j, T_2, edge37, edge38, edge32, edge31, edge34, edge39, edge40, edge33, edge35, edge41, U_2, edge42, edge36, V_2, face18, face20, face22, face19, face17, face21
  120. Prism(C_2, A_1, U, O_2, Q_2) → l, W_2, edge46, edge43, edge44, edge48, edge49, edge47, edge45, edge50, edge51, edge53, Z_2, edge54, edge52, A_3, face23, face26, face24, face25, face27, face28
  121. Midpoint(U, T) → B_3
  122. Midpoint(V, K) → C_3
  123. Prism(D_2, C_2, B_3, P_2, R_2, W) → n, D_3, face30, face34, edge58, edge59, edge63, edge62, edge61, edge55, edge60, edge66, E_3, edge64, edge65, edge56, edge67, edge68, edge69, edge57, F_3, G_3, face35, face29, face31, face33, face32
  124. Prism(A_1, C_2, O_2, B_2) → o, H_3, edge72, edge70, edge76, edge77, edge73, edge78, edge74, I_3, face36, face38, face40, face39, face37, edge71, edge75
  125. Prism(C_3, N_2, W, K, P_2) → r, J_3, edge83, edge81, edgeKW, edge79, edge85, edge84, edge82, edge80, edge86, edge88, K_3, edge89, edge87, L_3, face41, face45, face44, face42, face43, face46
  126. Prism(Q_2, K_3, Z, C_2, P_2) → s, M_3, edge98, edge91, edge90, edge93, edge95, edge99, edge92, edge94, edge96, edge100, N_3, edge101, edge97, O_3, face47, face51, face49, face48, face50, face52
  127. Prism(P_2, J_3, C_2, O_3, G_2) → t, P_3, edge108, edge102, edge103, edge109, edge105, edge110, edge104, edge111, edge106, edge112, Q_3, edge113, edge107, R_3, face53, face56, face54, face55, face57, face58
  128. Prism(V, N_2, D_2, B_1, U) → w, S_3, edge117, edge120, edge118, edge116, edgeUV, edge122, edge121, edge119, edge114, edge123, T_3, edge124, edge115, U_3, face62, face60, face64, face63, face59, face61
  129. Prism(S_3, U, T, K_2, R_2) → a_1, V_3, edge127, edgeTU, edge125, edge129, edge131, edge128, edge126, edge130, edge132, edge134, W_3, edge135, edge133, Z_3, face65, face68, face66, face67, face69, face70
  130. Prism(Z_3, R_2, S_3, K_2, E_2) → b_1, A_4, edge143, edge142, edge139, edge140, edge136, edge144, edge145, edge141, edge137, edge146, B_4, edge147, edge138, C_4, face74, face72, face76, face75, face71, face73