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Projection of a Cube on a Plane

Projection of a Cube on a Plane
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2019-05-24 15:01
Solid GeometryTransformationGeometric Construction
This example demonstrates the projection of a cube onto a plane. Key mathematical concepts include solid geometry and projection transformations. Using GeoGebra commands such as Circle, Point, Angle, Segment, etc., the construction of the cube and its projection is illustrated. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Circle(I_1, 0.6) → k_2
  2. Point(k_2) → K_1
  3. Point(k_2) → J_1
  4. Angle(J_1, I_1, K_1) → b_1
  5. Circle(I, 0.6) → k_1
  6. Point(k_1) → K
  7. Point(k_1) → J
  8. Angle(J, I, K) → a_1
  9. Segment(A', B') → i
  10. Segment(B', C') → j
  11. Segment(C', D') → k
  12. Segment(D', A') → l
  13. Segment(B', F') → m
  14. Segment(F', E') → n
  15. Segment(A', E') → p
  16. Segment(E', H') → r
  17. Segment(G', H') → s
  18. Segment(G', F') → t
  19. Segment(G', C') → i_1
  20. Segment(H', D') → j_1
  21. Ray(A', A) → l_1
  22. Ray(B', B) → m_1
  23. Ray(F', F) → n_1
  24. Ray(E', E) → p_1
  25. Ray(G', G) → q_1
  26. Ray(H', H) → r_1
  27. Ray(D', D) → s_1
  28. Ray(C', C) → t_1
  29. Ellipse(L, M, N) → p_2
  30. Segment(A, B) → c
  31. Segment(A, E) → d
  32. Segment(E, F) → e
  33. Segment(B, F) → f
  34. Segment(F, G) → g
  35. Segment(H, E) → h
  36. Segment(D, A) → c_1
  37. Segment(C, B) → d_1
  38. Segment(D, C) → e_1
  39. Segment(H, G) → f_1
  40. Segment(G, C) → g_1
  41. Segment(D, H) → h_1
  42. Polygon(A, B, C, D) → Vieleck1, a_2, b_2, c_2, d_2
  43. Polygon(A', B', C', D') → Vieleck2, a', b', c', d'
  44. Polygon(C, B, F, G) → Vieleck3, c_3, b_3, f_2, g_2
  45. Polygon(C', B', F', G') → Vieleck4, c'_1, b'_1, f', g'
  46. Polygon(C, D, H, G) → Vieleck5, c_4, d_3, h_2, g_3
  47. Polygon(C', G', H', D') → Vieleck6, c'_2, g'_1, h', d'_1
  48. Polygon(E, F, G, H) → Vieleck7, e_2, f_3, g_4, h_3
  49. Polygon(E', F', G', H') → Vieleck8, e', f'_1, g'_2, h'_1
  50. Polygon(A, B, F, E) → Vieleck9, a_3, b_4, f_4, e_3
  51. Polygon(A', B', F', E') → Vieleck10, a'_1, b'_2, f'_2, e'_1
  52. Polygon(A, D, H, E) → Vieleck11, a_4, d_4, h_4, e_4
  53. Polygon(A', D', H', E') → Vieleck12, a'_2, d'_2, h'_2, e'_2