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Cube of a Binomial

Cube of a Binomial
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2018-01-17 05:03
FunctionCoordinate GeometrySolid Geometry
This example demonstrates the cube of a binomial. It involves core concepts of polynomial expansion and solid geometry. Using GeoGebra commands such as Segment, Point, Polygon, Prism, etc., a clear cube model can be constructed. Suitable for high school mathematics education, helping students understand the basic principles of polynomial expansion and solid geometry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Point(f) → I
  3. Polygon(A, I, L, J) → q1, a_1, i, l, j
  4. Prism(q1, K) → b, P, edgeIP, edgeLQ, edgeJR, edgeKP, edgePQ, edgeQR, edgeKR, Q, R, faceAIPK, faceILQP, faceJLQR, faceAJRK, faceKPQR, edgeAK
  5. Prism(faceKPQR, D) → d, V, edgePV, edgeQW, edgeRZ, edgeDV, edgeVW, edgeWZ, edgeDZ, W, Z, faceDKPV, facePQWV, faceQRZW, faceDKRZ, faceDVWZ, edgeDK
  6. Min(1, A2) → A3
  7. Prism(faceILQP, B) → c, S, edgeLS, edgeQT, edgePU_1, edgeBS, edgeST, edgeTU, edgeBU, T, U, faceBILS, faceLQTS, facePQTU, faceBIPU, faceBSTU, edgeBI
  8. Prism(facePQWV, U) → e, A_1, edge1, edge5, edge4, edge2, edge6, edge7, edge3, B_1, C_1, face1, face3, face5, face2, face4, edgePU
  9. Prism(faceJLQR, D_1) → g, E_1, edge8, edge11, edge10, edge12, edge14, edge15, edge13, F_1, G_1, face6, face7, face9, face8, face10, edge9
  10. Prism(faceQRZW, G_1) → h, H_1, edge17, edge19, edge18, edge20, edge22, edge23, edge21, I_1, J_1, face11, face13, face14, face12, face15, edge16
  11. Prism(faceLQTS, D_1) → k, K_1, edge25, edge27, edge26, edge28, edge30, edge31, edge29, L_1, M_1, face16, face18, face19, face17, face20, edge24
  12. Prism(face3, K_1) → m, N_1, edge33, edge35, edge34, edge36, edge38, edge39, edge37, O_1, P_1, face21, face23, face24, face22, face25, edge32
  13. Midpoint(A, I) → Q_1
  14. Midpoint(I, B) → R_1
  15. Max(0, Min[1, A2 - 1]) → A4
  16. Max(0, Min[1, A2 - 2]) → A5
  17. Vector(A, A_2) → u
  18. Vector(A, D_2) → v
  19. Vector(A, E_2) → w
  20. Vector(A, H / 3) → n
  21. Translate(m, Vector[((3 * n) * A3)]) → m'
  22. Translate(c, Vector[(n * A3)]) → c'
  23. Translate(d, Vector[(n * A3)]) → d'
  24. Translate(e, Vector[((2 * n) * A3)]) → e'
  25. Translate(g, Vector[(n * A3)]) → g'
  26. Translate(h, Vector[((2 * n) * A3)]) → h'
  27. Translate(k, Vector[((2 * n) * A3)]) → k'
  28. Line(S_1, T_1) → p
  29. Line(T_1, U_1) → q
  30. Line(S_1, U_1) → r
  31. Midpoint(T_1, U_1) → V_1
  32. Ray(S_1, V_1) → s
  33. Ray(S_1, W_1) → t
  34. Angle(t, s) → α
  35. Rotate(d', (-((α * A4))), q) → d''
  36. Rotate(c', (-((α * A4))), p) → c''
  37. Rotate(g', (α * A4), r) → g''
  38. Vector(S_1, Z_1) → u_1
  39. Vector(T_1, Z_1) → v_1
  40. Vector(U_1, Z_1) → w_1
  41. Translate(q, w_1) → q'
  42. Translate(r, u_1) → r'
  43. Translate(p, v_1) → p'
  44. Rotate(e', (-((α * A4))), p') → e''
  45. Rotate(h', (-((α * A4))), q') → h''
  46. Rotate(k', (α * A4), r') → k''
  47. Translate(B, Vector[(n * A3)]) → B'
  48. Translate(I, Vector[(n * A3)]) → I'
  49. Segment(B', I') → edgeBI'
  50. Translate(S, Vector[(n * A3)]) → S'
  51. Translate(B, Vector[(n * A3)]) → B'_1
  52. Segment(S', B'_1) → edgeBS'
  53. Translate(B, Vector[(n * A3)]) → B'_2
  54. Translate(U, Vector[(n * A3)]) → U'
  55. Segment(B'_2, U') → edgeBU'
  56. Rotate(B', (-((α * A4))), p) → B''
  57. Rotate(I', (-((α * A4))), p) → I''
  58. Segment(B'', I'') → edgeBI''
  59. Rotate(S', (-((α * A4))), p) → S''
  60. Rotate(B'_1, (-((α * A4))), p) → B_2
  61. Segment(S'', B_2) → edgeBS''
  62. Rotate(B'_2, (-((α * A4))), p) → C_2
  63. Rotate(U', (-((α * A4))), p) → U''
  64. Segment(C_2, U'') → edgeBU''
  65. Vector(A, K) → b_1
  66. Translate(B, Vector[b_1 + ((2 * n) * A3)]) → B'_3
  67. Translate(I, Vector[b_1 + ((2 * n) * A3)]) → I'_1
  68. Segment(B'_3, I'_1) → edgeBI'_1
  69. Translate(S, Vector[b_1 + ((2 * n) * A3)]) → S'_1
  70. Translate(B, Vector[b_1 + ((2 * n) * A3)]) → B'_4
  71. Segment(S'_1, B'_4) → edgeBS'_1
  72. Translate(U, Vector[((2 * n) * A3)]) → U'_1
  73. Translate(C_1, Vector[((2 * n) * A3)]) → F_2
  74. Segment(U'_1, F_2) → edge3'
  75. Rotate(U'_1, (-((α * A4))), p') → G_2
  76. Rotate(F_2, (-((α * A4))), p') → H_2
  77. Segment(G_2, H_2) → edge3''
  78. Rotate(S'_1, (-((α * A4))), p') → I_2
  79. Rotate(B'_4, (-((α * A4))), p') → J_2
  80. Segment(I_2, J_2) → f_1
  81. Rotate(B'_3, (-((α * A4))), p') → K_2
  82. Rotate(I'_1, (-((α * A4))), p') → L_2
  83. Segment(K_2, L_2) → g_1
  84. Segment(B, I) → h_1
  85. Translate(Q, Vector[((3 * n) * A3)]) → Q'
  86. Translate(A_1, Vector[((3 * n) * A3)]) → M_2
  87. Segment(Q', M_2) → edge1'
  88. Translate(A_1, Vector[((3 * n) * A3)]) → N_2
  89. Translate(P_1, Vector[((3 * n) * A3)]) → O_2
  90. Segment(N_2, O_2) → edge34'
  91. Translate(B_1, Vector[((3 * n) * A3)]) → P_2
  92. Translate(A_1, Vector[((3 * n) * A3)]) → Q_2
  93. Segment(P_2, Q_2) → edge6'