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Create a Prism with Unity Cubes

Create a Prism with Unity Cubes
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2020-03-04 08:13
PolygonVectorTrigonometrySolid GeometryGeometric Construction
This example demonstrates how to create prisms using unit cubes to better understand the concept of volume. It involves core math concepts like volume, polygons, LCM and GCD, cosine, vectors 3D, and line segments. Key GeoGebra commands and objects used include Intersect, Vector, Segment, Line, Point, Polygon, Translate, and Sequence. Suitable for middle school and above, ideal for solid geometry instruction and volume concept reinforcement.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → H
  2. Vector(H, I) → u
  3. Segment(D, C) → b
  4. Segment(C, F) → f
  5. Segment(D, G) → g
  6. Segment(G, F) → h
  7. Segment(F, E) → i
  8. Line(E, F) → j
  9. Line(H, j) → k_1
  10. Segment(E, B) → a
  11. Segment(B, C) → c
  12. Point(yAxis) → A
  13. Vector(H, A) → v
  14. Vector(H, J) → w
  15. Polygon(B, C, F, E) → çokgen1, b_1, c_1, f_1, e_1
  16. Polygon(C, D, G, F) → çokgen2, c_2, d_1, g_1, f_2
  17. Polygon(B, K, D, C) → çokgen3, b_2, k_2, d, c_3
  18. Translate(B, u) → B'
  19. Translate(K, u) → K'
  20. Translate(D, u) → D'
  21. Translate(C, u) → C'
  22. Intersect(j, f) → L
  23. Intersect(g, h) → M
  24. Line(L, M) → q
  25. Translate(B, w) → B'_1
  26. Translate(K, w) → K'_1
  27. Translate(D, w) → D'_1
  28. Translate(C, w) → C'_1
  29. Translate(B', w) → B''
  30. Translate(K', w) → K''
  31. Translate(D', w) → D''
  32. Translate(C', w) → C''
  33. Translate(B'', w) → B'''
  34. Translate(K'', w) → K'''
  35. Translate(D'', w) → D'''
  36. Translate(C'', w) → C'''
  37. Translate(B''', w) → N
  38. Translate(K''', w) → O
  39. Translate(D''', w) → P
  40. Translate(C''', w) → Q
  41. Translate(N, w) → N'
  42. Translate(O, w) → O'
  43. Translate(P, w) → P'
  44. Translate(Q, w) → Q'
  45. Translate(B'', w) → B'''_1
  46. Translate(K'', w) → K'''_1
  47. Translate(D'', w) → D'''_1
  48. Translate(C'', w) → C'''_1
  49. Translate(B'''_1, w) → R
  50. Translate(K'''_1, w) → S
  51. Translate(D'''_1, w) → T
  52. Translate(C'''_1, w) → U
  53. Translate(R, w) → R'
  54. Translate(S, w) → S'
  55. Translate(T, w) → T'
  56. Translate(U, w) → U'
  57. Intersect(j, q) → V
  58. Intersect(b, f) → W
  59. Intersect(b_2, k_2) → Z_1
  60. Intersect(b_2, k_2) → K_1
  61. Translate(C, w) → C'_2
  62. Translate(D, w) → D'_2
  63. Translate(G, w) → G'
  64. Translate(F, w) → F'
  65. Sequence(Polygon[Translate[B, Vector[(i * u)]], Translate[K, Vector[(i * u)]], Translate[D, Vector[(i * u)]], Translate[C, Vector[(i * u)]]], i, 1, k - 1) → liste3
  66. Sequence(Translate[Element[liste1, 1], Vector[(i * u)]], i, 1, k - 1) → liste4
  67. Sequence(Polygon[Translate[B, Vector[(i * u)]], Translate[C, Vector[(i * u)]], Translate[F, Vector[(i * u)]], Translate[E, Vector[(i * u)]]], i, 1, k - 1) → liste5
  68. Sequence(Segment[Translate[F, Vector[(u * i)]], Translate[E, Vector[(u * i)]]], i, 0, k - 1) → liste10
  69. Sequence(Translate[liste10, Vector[(v * i)]], i, 1, o - 1) → liste11
  70. Sequence(Segment[Translate[G, Vector[(w * i)]], Translate[F, Vector[(w * i)]]], i, 0, m - 1) → liste12
  71. Sequence(Translate[liste12, Vector[(v * i)]], i, 1, o - 1) → liste13