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Open-Top Box

Open-Top Box
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2017-03-22 22:27
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the dynamic construction of an open-top rectangular prism. Key mathematical concepts include volume calculation in solid geometry and geometric construction. Using GeoGebra commands such as Intersect, Segment, and Point, the dimensions of the prism can be flexibly adjusted. Suitable for high school mathematics education and students learning solid geometry.

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

Draw an open-top rectangular prism to demonstrate its dynamic construction. Start by creating a rectangular base, then use reflection and rotation to generate the side and top faces, forming a prism with an open top. Key steps involve determining the vertices of the prism using coordinate geometry and constructing its faces through rotation and reflection, resulting in a dynamically adjustable open-top rectangular prism.
The prompt above was compiled from the original drawing commands and is for reference only.