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SolveMyMaths Action 1! Dynamic Area & Vector Geometry

SolveMyMaths Action 1! Dynamic Area & Vector Geometry
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2017-11-25 09:30
PolygonVectorGeometric ConstructionSlider Animation
① This example is a dynamic and modifiable geometric illustration of a problem posed by Ed Southall on Twitter, allowing users to explore changing configurations via sliders and draggable points. ② Core mathematical concepts include fractions, logical reasoning, addition, area computation, and vector operations, involving polygons, circles, sectors, and rotations. ③ Construction highlights: using GeoGebra commands such as Segment, Rotate, Angle, Ray, Point, Polygon, Circle, Intersect, CircleSector, Dilate, Vector, Translate, Min, Line, and Midpoint, the applet builds multiple points, segments, circles, sectors, and vectors, with dynamic parameters controlling the state. ④ Suitable for middle school and above, this is ideal for teachers and students to investigate area relationships, vector decomposition, and dynamic mathematical modeling, and can serve as a resource for math competitions or classroom discussions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Segment(A, C) → h
  7. Segment(C, B) → i
  8. Polygon(A, B, C) → t1, c, a_1, b
  9. Circle(A, (0.15 * Min[h, f])) → d
  10. Intersect(d, f) → D,
  11. Intersect(d, h) → E,
  12. CircleSector(A, D, E) → e
  13. Rotate(B, π / 3, C) → B'_1
  14. Rotate(C, π / 3, A) → C'
  15. Rotate(B, π / 3, A) → B'_2
  16. Rotate(A, If[0 < j ≤ 1, (j * π / 3), π / 3], A) → A'
  17. Rotate(C, If[0 < j ≤ 1, (j * π / 3), π / 3], A) → C'_1
  18. Segment(A', C'_1) → h'
  19. Rotate(C, If[0 < j ≤ 1, (j * π / 3), π / 3], C) → C'_2
  20. Rotate(B, If[0 < j ≤ 1, (j * π / 3), π / 3], C) → B'_3
  21. Segment(C'_2, B'_3) → i'
  22. Rotate(A, If[1 < j ≤ 2, ((-(j - 1)) * π / 3), ((-π)) / 3], C) → A'_1
  23. Rotate(C, If[1 < j ≤ 2, ((-(j - 1)) * π / 3), ((-π)) / 3], C) → C'_3
  24. Segment(A'_1, C'_3) → h'_1
  25. Rotate(C, If[1 < j ≤ 2, ((-(j - 1)) * π / 3), ((-π)) / 3], B) → C'_4
  26. Rotate(B, If[1 < j ≤ 2, ((-(j - 1)) * π / 3), ((-π)) / 3], B) → B'_4
  27. Segment(C'_4, B'_4) → i'_1
  28. Polygon(A, C, C'_1) → t2, c'_1, a_2, c_1
  29. Polygon(B, B'_3, C) → t3, c_2, b_1, b'_3
  30. Rotate(A, If[2 < j ≤ 3, ((j - 2) * π / 3), π / 3], A) → A'_2
  31. Rotate(B, If[2 < j ≤ 3, ((-(j - 2)) * π / 3), ((-π)) / 3], A) → B'_5
  32. Segment(A'_2, B'_5) → f'
  33. Rotate(A, If[3 < j ≤ 4, ((j - 3) * π / 3), π / 3], B) → A'_3
  34. Rotate(B, If[3 < j ≤ 4, ((-(j - 3)) * π / 3), ((-π)) / 3], B) → B'_6
  35. Segment(A'_3, B'_6) → f'_1
  36. Dilate(C'_1, If[5 < j ≤ 6, 6 - j, 0], B'_5) → F
  37. Vector(C'_1, F) → u
  38. Translate(A'_1, u) → G
  39. Translate(C'_3, u) → H
  40. Dilate(C, If[6 < j ≤ 7, 7 - j, 0], C'_1) → C'_5
  41. Vector(C, C'_5) → v
  42. Translate(C'_2, v) → I
  43. Translate(B'_3, v) → J
  44. Polygon(A, B'_5, B) → t4, b_2, a_3, b'_2
  45. Segment(A, B'_3) → l
  46. Segment(B, C'_1) → m
  47. Min(f, i) → n
  48. Min({f, i, h}) → o
  49. Circle(B, (0.2 * o)) → p
  50. Intersect(p, f, 1) → K
  51. Intersect(p, f'_1) → L,
  52. Intersect(p, m, 1) → M
  53. Circle(A, (0.2 * o)) → q
  54. Line(A, B'_3) → r
  55. Intersect(q, r, 1) → N
  56. Ray(A, N) → s
  57. Intersect(q, f') → O,
  58. Angle(O, A, B'_3) → β
  59. Angle(C'_1, B, L) → γ
  60. Dilate(B'_3, If[4 < j ≤ 5, 5 - j, 0], A) → A'_4
  61. Dilate(C'_1, If[5 < j ≤ 6, 6 - j, 0], B) → B'_7
  62. Rotate(L, If[6 < j ≤ 7, ((-(j - 6)) * γ), (-γ)], B) → L'
  63. CircleSector(B, L', L) → d_1
  64. Rotate(O, If[7 < j ≤ 8, ((j - 7) * β), β], A) → O'
  65. CircleSector(A, O, O') → e_1
  66. Midpoint(A, B) → P
  67. Line(P, s) → f_1
  68. Line(B, s) → g_1
  69. Point(g_1) → Q
  70. Angle(C'_1, B, Q) → δ
  71. Dilate(B, If[8 < j ≤ 9, 9 - j, 0], P) → B'_8
  72. Vector(B, B'_8) → w
  73. Translate(d_1, w) → h_1
  74. Rotate(h_1, If[9 < j ≤ 10, ((j - 9) * π / 3), π / 3], P) → k_1
  75. Dilate(P, If[10 < j ≤ 11, 11 - j, 0], A) → P'
  76. Vector(P, P') → u_1
  77. Translate(k_1, u_1) → p_1
  78. Segment(A, B) → i_1
  79. Segment(B'_3, A'_4) → j_1
  80. Segment(C'_1, B'_7) → t