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动态几何图形演示 by Tim Brzezinski (10)

动态几何图形演示 by Tim Brzezinski (10)
几何画板及绘图内容加载中，请稍等……
2018-06-06 10:03
圆向量解析几何最值优化几何作图
①本范例动态演示了二维空间中圆与向量的关系及几何变换现象；②涉及核心数学概念包括向量运算、几何变换（旋转、镜像、平移）、解析几何与积分优化；③作图要点提炼自构造摘要，使用GeoGebra命令如Circle, Vector, Rotate, Mirror, Translate等构建图形；④适合高中及以上数学学习，用于理解向量、变换及优化问题的直观表示。

GeoGebra 命令及参数

  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