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Dynamic Open-Top Rectangular Prism Box Construction

Dynamic Open-Top Rectangular Prism Box Construction
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2020-09-12 00:07
PolygonCoordinate GeometrySolid GeometryTransformationGeometric Construction
This example demonstrates how to construct a modifiable open-top rectangular prism (a box-like solid) and generate its boundary shapes using dynamic geometric operations. The key mathematical ideas include solid geometry with a rectangular prism, intersection of geometric elements to obtain edge/hinge lines, and using geometric transformations—mirror symmetry and rotation—to assemble consistent faces and an open-top configuration. Construction highlights: Intersect is used to compute intersection points/segments that define the structure; Segment and Point create and track the defining edges and vertices; Mirror produces symmetric counterparts of relevant parts; Circle provides auxiliary constraints/positions; Polygon builds the face outlines (such as the base and side regions); and Rotate reorients parts to complete the spatial arrangement. The model is organized from multiple construction points (e.g., A, B, E, F, H, I, J, K) and polygonal regions (e.g., poly2, poly3), including mirrored/rotated derived objects, to yield the final open-top box geometry. Suitable for middle school through early university levels, especially for dynamic geometry demonstrations, parameter-driven solid construction, and as a foundation for later volume/optimization discussions.

GeoGebra Commands & Parameters

  1. Intersect(l, xAxis) → E
  2. Intersect(j, l) → F
  3. Segment(A, F) → m
  4. Point(m) → G
  5. Mirror(G, j) → G'
  6. Mirror(G, k) → G'_1
  7. Mirror(G', k) → G''
  8. Segment(A, G) → n
  9. Circle(A, G) → c
  10. Intersect(c, r, 1) → H
  11. Intersect(p, s) → I
  12. Mirror(H, k) → H'
  13. Mirror(I, k) → I'
  14. Mirror(I, j) → I'_1
  15. Mirror(H, j) → H'_1
  16. Mirror(I'_1, k) → J
  17. Mirror(H'_1, k) → K
  18. Segment(I', J) → t
  19. Segment(J, I'_1) → a
  20. Segment(I'_1, I) → b
  21. Segment(I, I') → d
  22. Segment(A, B) → e
  23. Segment(A, H) → n_1
  24. Polygon(G, G', I'_1, I) → poly2, g_1, g', i'_1, i_1
  25. Polygon(I, H, H', I') → poly3, i_2, h_1, h', i'
  26. Polygon(I', G'_1, G'', J) → poly4, i'_2, g'_1, g'', j_1
  27. Polygon(J, K, H'_1, I'_1) → poly5, j_2, k_1, h'_1, i'_3
  28. Polygon(I, I'_1, J, I') → poly6, i_3, i'_4, j_3, i'_5
  29. Segment(I, I'_1) → p_1
  30. Segment(I'_1, J) → q_1
  31. Segment(J, I') → r_1
  32. Segment(I', I) → s_1
  33. Rotate(G, α, b) → G'_2
  34. Rotate(G', α, b) → G''_1
  35. Rotate(I'_1, α, b) → L
  36. Rotate(I, α, b) → I'_2
  37. Polygon(G'_2, G''_1, L, I'_2) → poly2', g'_2, g''_1, l_2, i'_6
  38. Rotate(J, α, x = x(J)) → J'
  39. Rotate(K, α, x = x(J)) → K'
  40. Rotate(I'_1, α, x = x(J)) → N
  41. Rotate(J, (-α), x = x(J)) → J'_1
  42. Rotate(K, (-α), x = x(J)) → K'_1
  43. Rotate(H'_1, (-α), x = x(J)) → O
  44. Rotate(I'_1, (-α), x = x(J)) → P
  45. Polygon(J'_1, K'_1, O, P) → poly5'_1, j'_1, k'_1, o, p_2
  46. Rotate(I', (-α), y = y(H')) → I''_1
  47. Rotate(G'_1, (-α), y = y(H')) → Q
  48. Rotate(G'', (-α), y = y(H')) → G'''_1
  49. Rotate(J, (-α), y = y(H')) → J'_3
  50. Polygon(I''_1, Q, G'''_1, J'_3) → poly4'_1, i''_1, q_2, g'''_1, j'_3
  51. Rotate(I, α, x = x(G)) → I'_3
  52. Rotate(H, α, x = x(G)) → H'_2
  53. Rotate(H', α, x = x(G)) → H''
  54. Rotate(I', α, x = x(G)) → I''
  55. Polygon(I'_3, H'_2, H'', I'') → poly3', i'_7, h'_2, h'', i''
  56. Rotate(A, ((-π)) / 2, B) → A'
  57. Rotate(B, ((-π)) / 2, B) → B'
  58. Segment(A', B') → e'
  59. Rotate(A', ((-π)) / 2, A') → A''
  60. Rotate(B', ((-π)) / 2, A') → B''
  61. Segment(A'', B'') → e''
  62. Rotate(A'', ((-π)) / 2, B'') → A'''
  63. Rotate(B'', ((-π)) / 2, B'') → B'''
  64. Segment(A''', B''') → e'''

AI Drawing Prompt Reference

This is a dynamic open-top rectangular prism box constructed using geometric operations. Key objects include points, line segments, circles, and polygons, which are connected through intersections to determine key positions, reflections to create symmetric parts, rotations to adjust spatial positions, and polygons to build the faces and edges of the box. The construction order is first finding key points via intersections, then creating symmetric structures through reflections, then adjusting positions with rotations, and finally combining polygons to form the complete open-top box geometry.
The prompt above was compiled from the original drawing commands and is for reference only.