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Three Planes Intersection Demo

Three Planes Intersection Demo
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2016-06-01 15:01
VectorSolid GeometryGeometric Construction
This example demonstrates the intersection points and geometric relationships among three planes in 3D space. It involves core mathematical concepts like spatial geometry, vector operations, cosine theorem, and trigonometric function characteristics. GeoGebra commands and objects used in construction include Circle, Point, Segment, Angle, Mirror, Translate, Polygon, and Vector. Suitable for high school geometry teaching and spatial vector applications.

GeoGebra Commands & Parameters

  1. Circle(A, B) → d
  2. Point(d) → C
  3. Segment(A, B) → e
  4. Segment(A, C) → f
  5. Angle(B, A, C) → α
  6. Mirror(D, (0, 0)) → F
  7. Mirror(E, (0, 0)) → G
  8. Segment(E, F) → g
  9. Segment(G, F) → h
  10. Segment(G, D) → i
  11. Segment(D, E) → j
  12. Translate(E, (0, 6)) → I
  13. Translate(F, (0, 6)) → J
  14. Segment(F, J) → l
  15. Segment(E, I) → k
  16. Translate(G, (0, 6)) → K
  17. Translate(D, (0, 6)) → H_1
  18. Segment(K, H_1) → i'
  19. Segment(H_1, D) → m
  20. Segment(K, G) → n
  21. Segment(I, H_1) → p
  22. Segment(J, K) → q
  23. Polygon(E, F, J, I) → poly1, e_1, f_1, j_1, i_1
  24. Polygon(F, G, K, J) → poly2, f_2, g_1, k_1, j_2
  25. Segment(I, K) → r
  26. Segment(E, G) → s
  27. Point(g) → H
  28. Vector(E, H) → u
  29. Translate(E, u) → E'
  30. Translate(G, u) → G'
  31. Segment(E', G') → s'
  32. Translate(E, u) → E'_1
  33. Translate(I, u) → I'
  34. Segment(E'_1, I') → k'
  35. Translate(I, u) → I'_1
  36. Translate(K, u) → K'
  37. Segment(I'_1, K') → r'
  38. Segment(K', G') → t
  39. Polygon(E, G, K, I) → poly3, e_2, g_2, k_2, i_2
  40. Polygon(E'_1, G', K', I'_1) → poly4, e'_1, g', k'_1, i'_1

AI Drawing Prompt Reference

Draw the intersection points and geometric relationships among three planes in 3D space to demonstrate core mathematical concepts. Start by creating a circle and a point on it, then form segments and angles. Use mirror operations and vector movements to generate multiple points and segments, creating several polygons. Finally, perform translation operations to create new points and segments, forming additional polygons to illustrate the spatial geometry and vector properties of the planes.
The prompt above was compiled from the original drawing commands and is for reference only.