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Projections of a Cube by Kristen Beck

Projections of a Cube by Kristen Beck
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2017-03-01 21:32
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the projections of a cube. It involves key concepts in solid geometry such as projection and planes. Using GeoGebra commands like Sphere, PointIn, Vector, etc., it dynamically shows the projections of a cube onto different planes. Suitable for high school geometry lessons.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), r) → s
  2. PointIn(s) → P
  3. Vector(P) → u
  4. OrthogonalPlane(P, u) → a
  5. Angle(Vector[Z], Vector[P]) → φ
  6. Angle(Vector[X], Vector[(x(P), y(P), 0)]) → θ
  7. Angle(Vector[X], Vector[(x(P), y(P), 0)]) → θ'
  8. If(y(P) ≥ 0, (((r * sin(φ + π / 2)) * cos(θ)), ((r * sin(φ + π / 2)) * sin(θ)), (r * cos(φ + π / 2))), (((r * sin(φ + π / 2)) * cos(θ')), ((r * sin(φ + π / 2)) * sin(θ')), (r * cos(φ + π / 2)))) → Q
  9. Vector(Q) → v
  10. OrthogonalPlane(Q, v) → b
  11. IntersectPath(a, b) → j
  12. Line(O, d) → f
  13. Intersect(f, s) → A, R
  14. Vector(R) → w
  15. OrthogonalPlane(R, w) → c
  16. IntersectPath(a, c) → k
  17. Intersect(j, k) → B
  18. IntersectPath(b, c) → g
  19. Cube(C, B, D) → e, E, face5, face6, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, G, edge9, edge10, edge11, edge12, H, I, J, face1, face2, face3, face4
  20. Segment(C', G') → h
  21. Segment(G', H') → i
  22. Segment(C', B') → l
  23. Segment(B', H') → m
  24. Segment(B', D') → n
  25. Segment(C', E') → p
  26. Segment(E', D') → q
  27. Segment(G', J') → t
  28. Segment(J', E') → f_1
  29. Segment(I', H') → g_1
  30. Segment(J', I') → h_1
  31. Intersect(F, Line[S, B]) → B''
  32. Intersect(F, Line[S, C]) → C''
  33. Intersect(F, Line[S, D]) → D''
  34. Intersect(F, Line[S, E]) → E''
  35. Intersect(F, Line[S, G]) → G''
  36. Intersect(F, Line[S, H]) → H''
  37. Intersect(F, Line[S, I]) → I''
  38. Intersect(F, Line[S, J]) → J''
  39. Segment(C'', G'') → i_1
  40. Segment(G'', H'') → j_1
  41. Segment(C'', B'') → k_1
  42. Segment(B'', H'') → l_1
  43. Segment(E'', D'') → m_1
  44. Segment(E'', J'') → n_1
  45. Segment(J'', I'') → p_1
  46. Segment(I'', D'') → q_1
  47. Segment(C'', E'') → r_1
  48. Segment(D'', B'') → s_1
  49. Segment(J'', G'') → t_1
  50. Segment(I'', H'') → a_1
  51. Segment(S, B'') → b_1
  52. Segment(S, C'') → c_1
  53. Segment(S, D'') → d_1
  54. Segment(S, E'') → e_1
  55. Segment(S, H'') → f_2
  56. Segment(S, G'') → g_2
  57. Segment(S, J'') → h_2
  58. Segment(S, E'') → i_2
  59. Segment(S, I'') → j_2

AI Drawing Prompt Reference

Draw a cube and show its projections onto different planes. Start by creating a sphere and selecting a point on it. Draw a vector through this point and create an orthogonal plane based on the vector. Calculate the angles with the coordinate axes, determine the projection points' coordinates, and draw the projection paths. Finally, combine the cube with the projection paths to display the projections onto various planes.
The prompt above was compiled from the original drawing commands and is for reference only.