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Volume and Polyhedron Construction in GeoGebra: Vectors, Polygons, and Sequences

Volume and Polyhedron Construction in GeoGebra: Vectors, Polygons, and Sequences
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2015-10-22 11:10
PolygonVectorSolid GeometryTransformationGeometric Construction
This GeoGebra example demonstrates a volume- and surface-related geometric construction, using points, segments, lines, polygons, vectors, and translations to build an interactive spatial figure, with sequences generating repeated objects. Core concepts include solid geometry, vectors, polygons, coordinate geometry, and geometric transformations. Construction highlights: Intersect finds intersection points; Vector, Segment, Line, and Point create basic elements; Polygon generates objects such as çokgen1, çokgen2, and çokgen3; Translate applies translations; Sequence organizes repeated structures. It is suitable for high-school or university lessons on volume, surface, vectors, and polyhedra, and as a GeoGebra geometric construction and dynamic modeling example.

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