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3D Ladder Model

3D Ladder Model
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2016-11-15 21:46
AngleSolid GeometryGeometric Construction
This example demonstrates the angle relationships between a ladder, wall, and floor in 3D, along with projection phenomena. Core math concepts include angle measurement, prism geometry, root calculations, exponential functions, and plane figures. GeoGebra commands and objects like Intersect, Point, Segment, Mirror, Plane, Line, Circle, Midpoint, and OrthogonalPlane are used in construction. Suitable for high school solid geometry and analytical geometry instruction, enhancing spatial visualization skills.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → B
  2. Point(xAxis) → A
  3. Segment(A, R) → f
  4. Point(f) → C
  5. Mirror(C, yAxis) → C'
  6. Point(zAxis) → J
  7. Segment(J, C) → g
  8. Mirror(J, zAxis) → J'
  9. Mirror(C, zAxis) → C'_1
  10. Segment(J', C'_1) → g'
  11. Plane(zAxis, yAxis) → a
  12. Line(J, yAxis) → h
  13. Circle(J, 4, a) → c
  14. Point(c) → D
  15. Line(D, g') → i
  16. Line(C', h) → j
  17. Midpoint(g') → E
  18. Midpoint(J, E) → F
  19. Midpoint(E, C') → G
  20. Line(F, j) → k
  21. Line(E, j) → l
  22. Line(G, j) → m
  23. Intersect(k, i) → H
  24. Intersect(i, l) → I
  25. Intersect(i, m) → K
  26. Intersect(i, j) → L
  27. Segment(J, D) → n
  28. Segment(D, L) → p
  29. Segment(F, H) → q
  30. Segment(E, I) → r
  31. Segment(G, K) → s
  32. Plane(zAxis, xAxis) → b
  33. Midpoint(g) → M
  34. Circle(M, 2, b) → d
  35. Intersect(zAxis, d) → N, O
  36. Segment(M, N) → t
  37. Midpoint(g') → P
  38. Segment(N, P) → e
  39. Plane(yAxis, xAxis) → o
  40. Mirror(D, a) → D'
  41. Mirror(L, a) → L'
  42. Segment(D', L') → p'
  43. Mirror(F, a) → F'
  44. Mirror(H, a) → H'
  45. Segment(F', H') → q'
  46. Mirror(E, a) → E'
  47. Mirror(I, a) → I'
  48. Segment(E', I') → r'
  49. Mirror(G, a) → G'
  50. Mirror(K, a) → K'
  51. Segment(G', K') → s'
  52. Midpoint(n) → Q
  53. OrthogonalPlane(Q, n) → u
  54. Mirror(M, u) → M'
  55. Mirror(N, u) → N'
  56. Segment(M', N') → t'
  57. Mirror(N, u) → N'_1
  58. Mirror(P, u) → P'
  59. Segment(N'_1, P') → e'
  60. Mirror(N, u) → N'_2

AI Drawing Prompt Reference

Draw a 3D ladder model showing the angle relationships between a ladder, wall, and floor, along with projection phenomena. Include a horizontal floor, a vertical wall, and a ladder with its base on the floor and top against the wall. Project the ladder's shadow onto the floor and mark key points, lines, and angles to demonstrate spatial geometry and projection effects.
The prompt above was compiled from the original drawing commands and is for reference only.