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Dynamic Geometry Demo: Power Functions & Similarity Transformation

Dynamic Geometry Demo: Power Functions & Similarity Transformation
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2018-06-16 09:16
PolygonFunctionCoordinate GeometryTransformationGeometric Construction
①This example dynamically illustrates a problem posted by Antonio Gutierrez on Twitter, involving power functions, linear equations, rhombus, polynomial functions, and similarity transformation; ②Core math concepts include function graphs, geometric transformations, similarity, and analytical geometry; ③Construction highlights utilize GeoGebra commands/objects such as Line, Rotate, Ray, Point, Segment, Polygon, Angle, Intersect, Min, Circle, Dilate, and CircleSector; ④Suitable for high school and above students to understand the relationship between function transformations and geometric figures.

GeoGebra Commands & Parameters

  1. Line(B, A) → f
  2. Rotate(A, (2 * π / 3), B) → B'
  3. Ray(B, B') → g
  4. Point(g) → C
  5. Ray(A, B) → h
  6. Segment(B, C) → i
  7. Segment(A, C) → j
  8. Polygon(B, A, C) → t1, c, a_1, b
  9. Rotate(A, π / 3, B) → B'_1
  10. Ray(B, B'_1) → k
  11. Angle(C, A, B) → α
  12. Rotate(C, α / 2, A) → C'
  13. Angle(C, A, C') → β
  14. Ray(A, C') → l
  15. Intersect(k, l) → I
  16. Min({Distance[B, A], i, j}) → d
  17. Circle(B, (0.2 * d)) → e
  18. Circle(A, (0.2 * d)) → p
  19. Intersect(e, h, 1) → E_1
  20. Intersect(p, j, 1) → F_1
  21. Ray(C, I) → m
  22. Intersect(h, m) → F
  23. Intersect(j, k) → E
  24. Intersect(g, l) → D
  25. Intersect(e, h, 2) → G
  26. Ray(B, G) → n
  27. Rotate(E_1, If[0 < a ≤ 1, (a * π / 3), π / 3], B) → H
  28. Dilate(B, If[0 < a ≤ 1, 1 - a, 0], I) → B'_2
  29. Segment(B, B'_2) → q
  30. CircleSector(B, E_1, H) → r
  31. Rotate(r, If[2 < a ≤ 3, ((a - 2) * π / 3), π / 3], B) → r'
  32. Rotate(r', If[4 < a ≤ 5, ((a - 4) * π / 3), π / 3], B) → r''
  33. Dilate(A, If[5 < a ≤ 6, 6 - a, 0], I) → A'
  34. Segment(A, A') → s
  35. Dilate(C, If[5 < a ≤ 6, 6 - a, 0], I) → C'_1
  36. Segment(C, C'_1) → t
  37. Rotate(F_1, If[5 < a ≤ 6, ((a - 5) * β), β], A) → J
  38. CircleSector(A, F_1, J) → c_1
  39. Rotate(c_1, If[7 < a ≤ 8, ((a - 7) * β), β], A) → d_1
  40. Dilate(I, If[8 < a ≤ 9, 9 - a, 0], E) → I'
  41. Dilate(I, If[8 < a ≤ 9, 9 - a, 0], F) → I'_1
  42. Dilate(I, If[8 < a ≤ 9, 9 - a, 0], D) → I'_2
  43. Segment(I, I') → f_1
  44. Segment(I, I'_1) → g_1
  45. Segment(I, I'_2) → h_1
  46. Dilate(A, If[9 < a ≤ 10, 10 - a, 0], F) → A'_1
  47. Dilate(C, If[9 < a ≤ 10, 10 - a, 0], D) → C'_2
  48. Segment(A, A'_1) → i_1
  49. Segment(C, C'_2) → j_1
  50. Angle(B, C, A) → γ
  51. Rotate(C, If[11 < a ≤ 12, ((a - 11) * γ), γ], C) → C'_3
  52. Rotate(C'_2, If[11 < a ≤ 12, ((a - 11) * γ), γ], C) → K
  53. Segment(C'_3, K) → k_1
  54. Rotate(A, If[12 < a ≤ 13, ((-(a - 12)) * α), (-α)], A) → A'_2
  55. Rotate(A'_1, If[12 < a ≤ 13, ((-(a - 12)) * α), (-α)], A) → L
  56. Segment(A'_2, L) → l_1
  57. Angle(I, E, L) → δ
  58. Rotate(I, If[13 < a ≤ 14, ((a - 13) * δ), δ], E) → I'_3
  59. Rotate(I', If[13 < a ≤ 14, ((a - 13) * δ), δ], E) → I''
  60. Segment(I'_3, I'') → m_1
  61. Rotate(I'_3, If[14 < a ≤ 15, ((a - 14) * π), π], E) → M
  62. Rotate(I'', If[14 < a ≤ 15, ((a - 14) * π), π], E) → I'''
  63. Segment(M, I''') → n_1