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Dynamic Geometry Illustration by Tim Brzezinski (7)

Dynamic Geometry Illustration by Tim Brzezinski (7)
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2018-06-06 10:03
CircleVectorCoordinate GeometryOptimizationGeometric Construction
This example dynamically demonstrates the relationship between circles and vectors in 2D space, including geometric transformations like rotation, reflection, and translation. It involves core math concepts such as vector operations, coordinate geometry, and integral optimization. Construction highlights include commands like Circle, Vector, Rotate, Mirror, and Translate from GeoGebra. Suitable for high school and above, helping visualize vector, transformation, and optimization problems.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. PointIn(a) → C
  3. Line(A, C) → f
  4. Intersect(c, f, 2) → D
  5. Circle(C, D) → d
  6. Tangent(c, d) → g, h, i, j
  7. Intersect(-6.398920282033919x² - 3.292519525505094x y + 0.6337072027875582y² + 100.00578631456865x + 27.07638245499153y = 371.2334325847297, c) → , , ,
  8. Intersect(c, h, 1) → E
  9. Intersect(c, g, 1) → F
  10. Intersect(d, g, 1) → G
  11. Intersect(d, h) → H
  12. Line(A, H) → k
  13. Line(C, E) → l
  14. Intersect(l, k) → I
  15. Line(A, G) → m
  16. Line(F, C) → n
  17. Angle(A, I, C) → α
  18. Intersect(m, n) → J
  19. Segment(A, C) → p
  20. Angle(F, J, G) → β
  21. Angle(C, J, A) → γ
  22. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], H) → A'
  23. Segment(A, A') → q
  24. Dilate(C, If[1 < b ≤ 2, 2 - b, 0], I) → C'
  25. Segment(C, C') → r
  26. Dilate(I, If[2 < b ≤ 3, 3 - b, 0], E) → I'
  27. Segment(I, I') → s
  28. Polygon(I, H, E) → t1, e, i_1, h_1
  29. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], G) → A'_1
  30. Segment(A, A'_1) → t
  31. Dilate(C, If[1 < b ≤ 2, 2 - b, 0], J) → C'_1
  32. Segment(C, C'_1) → f_1
  33. Dilate(J, If[2 < b < 3, 3 - b, 0], F) → J'
  34. Segment(J, J') → g_1
  35. Polygon(F, J, G) → t2, g_2, f_2, j_1
  36. Dilate(J, If[4 < b < 5, 5 - b, 0], I) → J'_1
  37. Vector(J, J'_1) → u
  38. Translate(F, u) → F'
  39. Translate(J, u) → J'_2
  40. Translate(G, u) → G'
  41. Mirror(J, g) → J'_3
  42. Dilate(J, If[4 < b < 5, 5 - b, 0], J'_3) → J'_4
  43. Polygon(F, J'_4, G) → t3, g_3, f_3, j'_4
  44. Angle(J'_3, F, J) → ε
  45. Angle(J, G, J'_3) → ζ
  46. Rotate(J, If[5 < b ≤ 6, ((-(b - 5)) * ε), (-ε)], F) → J'_5
  47. Rotate(J, If[5 < b ≤ 6, ((b - 5) * ζ), ζ], G) → J'_6
  48. Segment(F, J'_5) → l_1
  49. Segment(G, J'_6) → m_1
  50. Dilate(J'_3, If[7 < b ≤ 8, 8 - b, 0], I) → M
  51. Vector(J'_3, M) → v
  52. Translate(F, v) → F'_1
  53. Translate(J'_4, v) → N
  54. Translate(G, v) → G'_1
  55. Polygon(F'_1, N, G'_1) → t3', g'_1, f'_1, n_1
  56. Line(I, l_1) → k_1
  57. Point(k_1) → K
  58. Angle(E, I, K) → δ
  59. Rotate(F'_1, If[8 < b ≤ 9, ((-(b - 8)) * δ), (-δ)], I) → L
  60. Rotate(N, If[8 < b ≤ 9, ((-(b - 8)) * δ), (-δ)], I) → N'
  61. Rotate(G'_1, If[8 < b ≤ 9, ((-(b - 8)) * δ), (-δ)], I) → O
  62. Polygon(L, N', O) → t3'', o, l_2, n'
  63. Distance(F, G) → distanceFG
  64. Distance(A, C) → distanceAC
  65. Distance(C, I) → distanceCI
  66. Distance(G, J'_3) → distanceGJ'3
  67. Distance(J'_3, F) → distanceJ'3F
  68. Distance(I, A) → distanceIA
  69. Segment(A, C) → p_1
  70. Angle(J, A, C) → η
  71. Angle(A, C, J) → θ
  72. Segment(F, G) → q_1