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Animation 120: 2D Vectors and Polygon Construction

Animation 120: 2D Vectors and Polygon Construction
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2016-10-09 12:04
PolygonVectorTrigonometryCoordinate Geometry
In collections CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
①This example demonstrates the dynamic relationship between 2D vectors, polygons (like trapezoids), and circles through animation; ②Core mathematical concepts include trigonometric functions, 2D vector operations, real numbers, logarithmic functions, and statistical characteristics; ③Construction highlights the use of GeoGebra commands such as Polygon, Segment, Circle, Intersect, CircleSector, Dilate, Rotate, Line, Vector, Translate, and CircleArc; ④Suitable for high school and above students to understand dynamic changes in vectors, geometric transformations, and function graphs.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Polygon(B, E, 4) → poly2, j, k, l, m, G, H
  3. Polygon(E, F, 4) → poly3, n, p, q, r, I, J
  4. Segment(A, B) → s
  5. Segment(B, C) → t
  6. Segment(C, D) → b
  7. Segment(D, A) → c
  8. Segment(C, G) → d
  9. Segment(G, E) → e
  10. Segment(E, B) → f_1
  11. Segment(G, I) → g_1
  12. Segment(I, F) → h_1
  13. Segment(F, E) → i_1
  14. Angle(C, B, A) → α
  15. Angle(D, C, B) → β
  16. Angle(A, D, C) → γ
  17. Angle(C, G, E) → δ
  18. Angle(G, E, B) → ε
  19. Angle(I, F, E) → ζ
  20. Circle(A, (0.25 * b)) → c_1
  21. Circle(B, (0.25 * b)) → d_1
  22. Circle(E, (0.25 * b)) → e_1
  23. Segment(E, I) → j_1
  24. Segment(B, I) → k_1
  25. Segment(A, I) → l_1
  26. Intersect(c_1, l_1, 1) → K
  27. Intersect(c_1, s, 1) → L
  28. Intersect(d_1, k_1, 1) → M
  29. Intersect(d_1, f_1, 1) → N
  30. Intersect(e_1, j_1, 1) → O
  31. Intersect(e_1, i_1, 1) → P
  32. Intersect(e_1, e, 1) → Q
  33. CircleSector(B, N, M) → p_1
  34. CircleSector(A, L, K) → q_1
  35. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], I) → A'
  36. Segment(A, A') → m_1
  37. Dilate(I, If[1 < o ≤ 2, 2 - o, 0], B) → I'
  38. Segment(I, I') → n_1
  39. Dilate(E, If[2 < o ≤ 3, 3 - o, 0], I) → E'
  40. Segment(E, E') → s_1
  41. CircleSector(E, O, Q) → r_1
  42. Rotate(r_1, If[4 < o ≤ 5, ((-(o - 4)) * π / 4), ((-π)) / 4], E) → t_1
  43. Line(B, s_1) → a_1
  44. Intersect(a_1, m_1) → S
  45. Angle(N, B, S) → η
  46. Rotate(p_1, If[5 < o ≤ 6, ((o - 5) * η), η], B) → c_2
  47. Dilate(B, If[6 < o ≤ 7, 7 - o, 0], E) → B'
  48. Vector(B, B') → u
  49. Translate(c_2, u) → d_2
  50. CircleArc(B, N, M) → e_2
  51. Line(A, s_1) → b_1
  52. Angle(M, B, S) → θ
  53. Angle(L, A, K) → ι
  54. Rotate(q_1, If[7 < o ≤ 8, ((o - 7) * (π / 2 - θ)), π / 2 - θ], A) → f_2
  55. Dilate(A, If[8 < o ≤ 9, 9 - o, 0], E) → A'_1
  56. Vector(A, A'_1) → v
  57. Translate(f_2, v) → g_2
  58. CircleArc(A, L, K) → h_2