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Rectangular Prism Cross Sections by Nicolas ERDRICH

Rectangular Prism Cross Sections by Nicolas ERDRICH
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2012-02-23 02:51
VectorTrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the changing cross-sectional shapes of a rectangular prism at different angles. It involves core math concepts like solid geometry, vector operations, trigonometry, and coordinate geometry. Construction uses commands like Sequence, Element, Point, Polygon, Segment, Intersect, Line. Suitable for high school and above for understanding spatial geometry and cross-section analysis.

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

AI Drawing Prompt Reference

This is a geometric figure demonstrating the changing cross-sectional shapes of a rectangular prism at different angles. The figure is generated from a cube, using a sequence of points to define the sections. Key objects include a cube, a point C, a point J, a point K, a point L, and multiple polygons such as poly7, poly8, poly9, which represent different cross-sectional shapes. The construction order starts from generating a point list from the cube, then creating these polygons, and finally connecting points with line segments to define the figure structure. The figure illustrates spatial geometry and cross-section analysis concepts, suitable for high school and above.
The prompt above was compiled from the original drawing commands and is for reference only.