MathPlotAI Logo MathPlotAI

Demonstration of Rectangular Prism Sections

Demonstration of Rectangular Prism Sections
Loading the math board and drawing, please wait…
2014-11-11 04:55
VectorTrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the changing cross-sectional shapes of a rectangular prism at different angles. It involves core mathematical concepts such as solid geometry, vector operations, trigonometry, and 3D coordinate transformations. Construction highlights include the use of GeoGebra commands like Sequence, Element, Point, Polygon, Segment, Intersect, Line, along with objects like vectors u, v, w and rotation matrices R_x, R_y, R_z. It is suitable for high school students and math enthusiasts exploring spatial geometry and transformations.

GeoGebra Commands & Parameters

  1. Sequence(Mat * Element[cube, k], k, 1, 8) → cube'
  2. Element(Element[AE, 3], 1) → droite
  3. Sequence(I + (Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
  4. Point(listepoints) → C
  5. Element(AB, 3, 1) → avant
  6. Element(AC, 3, 1) → dessus
  7. Point(listepoints) → J
  8. Point(listepoints) → K
  9. Point(listepoints) → L
  10. Polygon(J, K, L, C) → poly7, j_2, k_1, l_1, c_5
  11. Point(listepoints) → M
  12. Point(listepoints) → N
  13. Polygon(J, M, N, K) → poly8, j_3, m_1, n_1, k_2
  14. Point(listepoints) → Q
  15. Polygon(K, L, Q, N) → poly9, k_3, l_2, q_1, n_2
  16. Point(listepoints) → A
  17. Polygon(J, C, A, M) → poly1, j, c, a_1, m
  18. Polygon(Q, A, C, L) → poly2, q, a_2, c_1, l
  19. Polygon(A, Q, N, M) → poly3, a_3, q_2, n, m_2
  20. Segment(A, M) → a'_1
  21. Segment(J, C) → j'_1
  22. Segment(K, L) → k'_3
  23. Segment(L, Q) → l'_2
  24. Segment(M, J) → m'
  25. Segment(N, K) → n'_2
  26. Segment(Q, N) → q'_1
  27. Segment(M, N) → m'_1
  28. Segment(Q, A) → q'
  29. Segment(K, J) → j'
  30. Segment(N, K) → l'
  31. Segment(C, L) → l''
  32. Segment(C, A) → l''''
  33. Segment(M, N) → k''''
  34. Segment(C, A) → k'''
  35. Point(j_3) → B
  36. Point(l_1) → D
  37. Point(n_1) → E
  38. Intersect(l_1, k_1) → F
  39. Intersect(c_5, l_1) → G
  40. Line(F, G) → d
  41. Segment(B, E) → e
  42. Line(D, e) → f
  43. Intersect(f, c) → H
  44. Segment(H, D) → g
  45. Segment(B, H) → h
  46. Line(E, h) → i
  47. Intersect(d, i) → O
  48. Intersect(i, k_1) → R
  49. Segment(R, D) → k
  50. Segment(E, R) → p
  51. Line(D, e) → r
  52. Intersect(r, l'_2) → S
  53. Segment(E, S) → s
  54. Line(B, s) → t
  55. Intersect(t, c_5) → T
  56. Segment(T, D) → b_1
  57. Segment(B, T) → d_1
  58. Segment(D, S) → e_1
  59. Polygon(B, E, S, D, T) → poly4, b_2, e_2, s_1, d_2, t_1
  60. Polygon(B, E, R, D, H) → poly5, b_3, e_3, r_1, d_3, h_1