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Position Relationship of Two Planes

Position Relationship of Two Planes
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2017-11-09 16:54
VectorSolid GeometryGeometric Construction
This example demonstrates the position relationship between two planes. Key mathematical concepts include the definition of a plane, rotation or rotation, and basic concepts in solid geometry. Using GeoGebra commands such as Cube, Polygon, Point, Plane, Intersect, etc., a cube can be constructed and the positional relationship between its faces can be observed. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Cube(A, B, C) → a, D, FlächeCDHG, FlächeEFGH, KanteAD, KanteAB, KanteBC, KanteCD, KanteAE, KanteDH, KanteEH, KanteEF, E, KanteBF, KanteFG, KanteCG, KanteGH, F, G, H, FlächeABCD, FlächeADHE, FlächeABFE, FlächeBCGF
  2. Polygon(B, F, G, C) → v2, b, f_1, g, c
  3. Point(KanteBF) → J
  4. Polygon(A, E, H, D) → v1, a_1, e, h, d
  5. Point(KanteAE) → I
  6. Point(KanteAE) → K
  7. Point(KanteBF) → L
  8. Point(KanteCG) → Q
  9. Plane(round((K * 100)) / 100, round((L * 100)) / 100, round((Q * 100)) / 100) → i
  10. Intersect(zAxis, xAxis) → M
  11. Point(xAxis) → N
  12. Vector(M, N) → u
  13. Point(yAxis) → O
  14. Vector(M, O) → v
  15. Point(zAxis) → P
  16. Vector(M, P) → w
  17. PointIn(i) → T
  18. OrthogonalVector(i) → j
  19. Point(KanteCG) → S
  20. Plane(round((I * 100)) / 100, round((J * 100)) / 100, round((S * 100)) / 100) → f
  21. PointIn(f) → U
  22. IntersectPath(i, f) → l
  23. Intersect(i, KanteAD) → V1
  24. Intersect(i, KanteCD) → V2
  25. Segment(K, L) → m
  26. Segment(L, Q) → n
  27. Segment(Q, V2) → p
  28. Segment(V2, V1) → q
  29. Segment(V1, K) → r
  30. Intersect(i, KanteDH) → V3
  31. Segment(K, V3) → s
  32. Segment(V3, Q) → t
  33. Intersect(f, KanteDH) → V4
  34. Segment(J, S) → g_1
  35. Segment(S, V4) → h_1
  36. Segment(V4, I) → i_1
  37. Segment(I, J) → j_1
  38. Intersect(f, KanteEH) → V5
  39. Intersect(f, Segment[G, H]) → V6
  40. Segment(I, V5) → k_1
  41. Segment(V5, V6) → l_1
  42. Segment(S, V6) → m_1
  43. Intersect(f, KanteCD) → V7
  44. Intersect(f, KanteAD) → V8
  45. Segment(S, V7) → n_1
  46. Segment(V7, V8) → p_1
  47. Segment(V8, I) → q_1
  48. Intersect(i, KanteGH) → V9
  49. Intersect(i, KanteEH) → VA
  50. Segment(Q, V9) → r_1
  51. Segment(V9, VA) → s_1
  52. Segment(VA, K) → t_1