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Demonstration of Two Parts of a Cube

Demonstration of Two Parts of a Cube
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2019-04-24 15:57
Solid GeometryProbability & StatisticsGeometric Construction
In collections TWO PARTS OF A CUBE
This example demonstrates the different parts of a cube and their geometric relationships. It involves core mathematical concepts such as solid geometry, surface area, similar triangles, correlation, normal distribution, and hypergeometric distribution. The construction uses GeoGebra commands and objects like Point, Cube, Intersect, Line, Rotate, Midpoint, and Prism. It is suitable for high school and above students learning complex geometric structures and probability statistics applications.

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) → a, D, faceCDHG, faceEFGH, edgeAD_1, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH_1, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Point(xAxis) → I
  6. Point(xAxis) → J
  7. Point(Circle[J, Distance[I, J], Segment[I, J]]) → K
  8. Cube(I, J, K) → b, L, faceKLPO, faceMNOP, edgeIL, edgeIJ, edgeJK_1, edgeKL, edgeIM, edgeLP, edgeMP, edgeMN, M, edgeJN, edgeNO, edgeKO, edgeOP, N, O, P, faceIJKL, faceILPM, faceIJNM, faceJKON
  9. Intersect(yAxis, xAxis) → Q
  10. Point(xAxis) → R
  11. Point(Circle[R, Distance[Q, R], Segment[Q, R]]) → S
  12. Cube(Q, R, S) → c, T, faceSTZW, faceUVWZ, edgeQT, edgeQR, edgeRS_1, edgeST, edgeQU, edgeTZ, edgeUZ, edgeUV, U, edgeRV, edgeVW, edgeSW, edgeWZ, V, W, Z, faceQRST, faceQTZU, faceQRVU, faceRSWV
  13. Point(xAxis) → A_1
  14. Point(xAxis) → B_1
  15. Point(Circle[B_1, Distance[A_1, B_1], Segment[A_1, B_1]]) → C_1
  16. Cube(A_1, B_1, C_1) → d, D_1, face5, face6, edge2, edge1, edge4, edge6, edge3, edge8, edge10, edge9, E_1, edge5, edge11, edge7, edge12, F_1, G_1, H_1, face1, face3, face2, face4
  17. Point(xAxis) → I_1
  18. Point(xAxis) → J_1
  19. Point(Circle[J_1, Distance[I_1, J_1], Segment[I_1, J_1]]) → K_1
  20. Cube(I_1, J_1, K_1) → e, L_1, face11, face12, edge14, edge13, edge16, edge18, edge15, edge20, edge22, edge21, M_1, edge17, edge23, edge19, edge24, N_1, O_1, P_1, face7, face9, face8, face10
  21. Line(A, yAxis) → f
  22. Line(I, yAxis) → g
  23. Line(A_1, yAxis) → h
  24. Line(I_1, yAxis) → i
  25. Line(A, zAxis) → j
  26. Line(I, zAxis) → k
  27. Line(A_1, zAxis) → l
  28. Line(I_1, zAxis) → m
  29. Rotate(a, α, f) → a'
  30. Rotate(a', β, xAxis) → a''
  31. Rotate(a'', γ, j) → a'''
  32. Rotate(b, δ, g) → b'
  33. Rotate(b', ε, xAxis) → b''
  34. Rotate(b'', ζ, k) → b'''
  35. Rotate(c, (-η), yAxis) → c'
  36. Rotate(c', θ, xAxis) → c''
  37. Rotate(c'', ι, zAxis) → c'''
  38. Rotate(d, κ, h) → d'
  39. Rotate(d', λ, xAxis) → d''
  40. Rotate(d'', μ, l) → d'''
  41. Rotate(e, ν, i) → e'
  42. Rotate(e', ξ, xAxis) → e''
  43. Rotate(e'', ο, m) → e'''
  44. Midpoint(A, B) → Q_1
  45. Midpoint(D, C) → R_1
  46. Midpoint(F, A) → S_1
  47. Midpoint(D, G) → T_1
  48. Midpoint(E, F) → U_1
  49. Prism(D, R_1, Q_1, A, H) → n, V_1, edge27, edge30, edge25, edgeAD, edgeDH, edge32, edge31, edge26, edge28, edge33, W_1, edge34, edge29, Z_1, face14, face16, face18, face15, face13, face17
  50. Prism(W_1, F, S_1, V_1) → o, A_2, edge38, edge40, edge37, edge39, edge41, edge43, edge42, B_2, face19, face22, face21, face23, face20, edge36, edge35
  51. Rotate(n, α, f) → n'
  52. Rotate(n', β, xAxis) → n''
  53. Rotate(n'', γ, j) → n'''
  54. Rotate(o, α, f) → o'
  55. Rotate(o', β, xAxis) → o''
  56. Rotate(o'', γ, j) → o'''
  57. Midpoint(N, J) → C_2
  58. Midpoint(O, K) → D_2
  59. Midpoint(M, N) → E_2
  60. Midpoint(P, O) → F_2
  61. Midpoint(I, J) → G_2
  62. Midpoint(L, K) → H_2
  63. Midpoint(M, I) → I_2
  64. Midpoint(I_2, C_2) → J_2
  65. Midpoint(P, L) → K_2
  66. Midpoint(K_2, D_2) → L_2
  67. Prism(G_2, J, K, H_2, J_2) → p, M_2, edge44, edgeJK, edge46, edge48, edge49, edge45, edge47, edge50, edge51, edge53, N_2, edge54, edge52, O_2, face24, face26, face25, face27, face28, face29
  68. Prism(F_2, O_2, N_2, E_2) → q, P_2, edge58, edge55, edge62, edge61, edge56, edge63, edge57, Q_2, face31, face33, face34, face32, face30, edge59, edge60
  69. Rotate(p, δ, g) → p'
  70. Rotate(p', ε, xAxis) → p''
  71. Rotate(q, δ, g) → q'
  72. Midpoint(V, R) → R_2
  73. Midpoint(R, Q) → S_2
  74. Midpoint(U, V) → T_2
  75. Midpoint(T_2, S_2) → U_2
  76. Midpoint(S, W) → V_2
  77. Midpoint(T, S) → W_2
  78. Prism(S_2, R, S, W_2, U_2) → r, Z_2, edge64, edgeRS, edge66, edge69, edge68, edge65, edge67, edge72, edge70, edge73, A_3, edge74, edge71, B_3, face35, face37, face36, face38, face39, face40
  79. Prism(Z_2, A_3, W, U_2) → s, C_3, edge75, edge78, edge82, edge77, edge79, edge83, edge80, D_3, face41, face45, face44, face43, face42, edge81, edge76
  80. Rotate(r, (-η), yAxis) → r'
  81. Rotate(r', θ, xAxis) → r''
  82. Rotate(r'', ι, zAxis) → r'''
  83. Rotate(s, (-η), yAxis) → s'
  84. Rotate(s', θ, xAxis) → s''
  85. Rotate(s'', ι, zAxis) → s'''
  86. Midpoint(A_1, B_1) → E_3
  87. Midpoint(B_1, F_1) → F_3
  88. Midpoint(E_1, A_1) → G_3
  89. Midpoint(G_3, F_3) → H_3
  90. Midpoint(D_1, A_1) → I_3
  91. Midpoint(C_1, B_1) → J_3
  92. Midpoint(J_3, I_3) → K_3
  93. Prism(A_1, I_3, J_3, B_1, G_3) → t, L_3, edge86, edge91, edge87, edge84, edge85, edge92, edge93, edge88, edge89, edge94, M_3, edge95, edge90, N_3, face46, face48, face51, face49, face47, face50
  94. Midpoint(L_3, M_3) → O_3
  95. Midpoint(F_1, G_1) → P_3
  96. Prism(O_3, P_3, M_3, H_3) → u, Q_3, edge99, edge96, edge103, edge101, edge97, edge104, edge98, R_3, face53, face55, face56, face54, face52, edge102, edge100
  97. Rotate(t, κ, h) → t'
  98. Rotate(t', λ, xAxis) → t''
  99. Rotate(t'', μ, l) → t'''
  100. Rotate(u, κ, h) → u'
  101. Rotate(u', λ, xAxis) → u''
  102. Rotate(u'', μ, l) → u'''
  103. Midpoint(P_1, O_1) → S_3
  104. Midpoint(M_1, N_1) → T_3
  105. Midpoint(L_1, K_1) → U_3
  106. Midpoint(I_1, J_1) → V_3
  107. Midpoint(P_1, M_1) → W_3
  108. Midpoint(O_1, N_1) → Z_3
  109. Midpoint(Z_3, W_3) → A_4
  110. Midpoint(L_1, I_1) → B_4
  111. Midpoint(K_1, J_1) → C_4
  112. Midpoint(C_4, B_4) → D_4
  113. Prism(L_1, B_4, D_4, U_3, P_1) → v, E_4, edge107, edge112, edge110, edge106, edge105, edge113, edge114, edge111, edge108, edge115, F_4, edge116, edge109, G_4, face59, face57, face62, face61, face58, face60
  114. Midpoint(F_4, D_4) → H_4
  115. Midpoint(G_4, U_3) → I_4
  116. Prism(U_3, K_1, I_4, D_4) → w, J_4, edge121, edge120, edge119, edge124, edge122, edge125, edge123, K_4, face63, face65, face66, face67, face64, edge117, edge118
  117. Rotate(v, ν, i) → v'
  118. Rotate(w, ν, i) → w'
  119. Rotate(v', ξ, xAxis) → v''
  120. Rotate(w', ξ, xAxis) → w''
  121. Rotate(v'', ο, m) → v'''
  122. Rotate(w'', ο, m) → w'''
  123. Point(k) → L_4
  124. Point(b''') → Q_4
  125. Point(b''') → R_4
  126. Point(b''') → S_4
  127. Point(b''') → T_4
  128. Prism(H_2, L_2, K_2, M_4, G_2) → a_1, N_4, edge129, edge131, edge132, edge130, edge126, edge134, edge133, edge135, edge127, edge136, O_4, edge137, edge128, P_4, face71, face68, face72, face73, face69, face70
  129. Rotate(a_1, δ, g) → b_1
  130. Rotate(b_1, ε, xAxis) → c_1
  131. Rotate(c_1, ζ, k) → d_1
  132. Prism(U_4, K_2, L_2, L_4) → e_1, V_4, edge141, edge143, edge140, edge142, edge144, edge146, edge145, W_4, face74, face77, face76, face78, face75, edge139, edge138
  133. Rotate(e_1, δ, g) → f_1
  134. Rotate(f_1, ε, xAxis) → g_1
  135. Rotate(g_1, ζ, k) → h_1

AI Drawing Prompt Reference

Draw two cubes, then rotate each cube around the Y-axis, X-axis, and Z-axis at different angles to show the rotated cubes. Draw three lines parallel to the X-axis, Y-axis, and Z-axis, and mark their intersection point. Finally, calculate and label the midpoints of the cube's edges to demonstrate their relationships with the cube.
The prompt above was compiled from the original drawing commands and is for reference only.