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Animation Demonstrating Polygons and 3D Vectors

Animation Demonstrating Polygons and 3D Vectors
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2016-06-14 22:44
PolygonAngleVectorSolid GeometryGeometric Construction
This example demonstrates the relationship between polygons and 3D vectors through animation, showcasing rotation, angle measurement, and geometric transformations in three-dimensional space. It involves core mathematical concepts such as polygon construction, 3D vector operations, angle measurement, and rotational transformations. The construction utilizes GeoGebra commands and objects like Circle, Point, Line, Rotate, Angle, CircleArc, Ray, Intersect, CircleSector, and Polygon. Suitable for high school and above students studying solid geometry, vector properties, and polygon characteristics, as well as for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Circle(A, 8 - a) → c
  2. Point(c) → B
  3. Line(A, B) → b
  4. Rotate(B, 60°, A) → B'
  5. Angle(B, A, B') → α
  6. Rotate(B', 60°, A) → B''
  7. Angle(B', A, B'') → β
  8. Rotate(B'', 60°, A) → B'''
  9. Angle(B'', A, B''') → γ
  10. Rotate(B''', 60°, A) → C
  11. Angle(B''', A, C) → δ
  12. Rotate(C, 60°, A) → C'
  13. Angle(C, A, C') → ε
  14. CircleArc(A, B, B') → d
  15. CircleArc(A, B', B'') → e
  16. CircleArc(A, B'', B''') → f
  17. CircleArc(A, B''', C) → g
  18. CircleArc(A, C, C') → h
  19. CircleArc(A, C', B) → k
  20. Point(d) → D
  21. Point(e) → E
  22. Point(f) → F
  23. Point(g) → G
  24. Point(h) → H
  25. Point(k) → I
  26. Ray(D, E) → i
  27. Ray(E, F) → j
  28. Ray(F, G) → l
  29. Ray(G, H) → m
  30. Ray(H, I) → n
  31. Ray(I, D) → p
  32. Circle(E, 1.5) → q
  33. Circle(F, 1.5) → r
  34. Circle(G, 1.5) → s
  35. Circle(H, 1.5) → t
  36. Circle(I, 1.5) → c_1
  37. Circle(D, 1.5) → d_1
  38. Intersect(r, j, 1) → J
  39. Intersect(r, l, 1) → K
  40. Intersect(s, l, 2) → L
  41. Intersect(s, m, 1) → M
  42. Intersect(r, j, 2) → N
  43. Intersect(t, m, 2) → O
  44. Intersect(t, n, 1) → P
  45. Intersect(c_1, n, 2) → Q
  46. Intersect(c_1, p, 1) → R
  47. Intersect(d_1, p, 2) → S
  48. Intersect(d_1, i, 1) → T
  49. Intersect(q, j, 1) → U
  50. Intersect(q, i, 2) → V
  51. CircleSector(F, N, K) → e_1
  52. CircleSector(G, L, M) → f_1
  53. CircleSector(H, O, P) → g_1
  54. CircleSector(I, Q, R) → h_1
  55. CircleSector(D, S, T) → k_1
  56. CircleSector(E, V, U) → p_1
  57. Polygon(G, H, I, D, E, F) → poly1, g_2, h_2, i_1, d_2, e_2, f_2