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几何均值趣谈

几何均值趣谈
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2017-08-04 09:08
圆向量几何作图
本范例动态展示了某段长度为两段长度几何均值的线段。涉及几何均值的概念。通过使用GeoGebra命令如Circle, Point, Line等进行构造。适合初中及以上学生学习几何均值概念。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Line(A, C) → f
  4. OrthogonalLine(C, f) → g
  5. Intersect(c, f, 2) → D
  6. CircleArc(A, D, C) → d
  7. CircleArc(A, C, D) → e
  8. Point(d) → E
  9. Point(e) → F
  10. OrthogonalLine(F, g) → h
  11. OrthogonalLine(E, g) → i
  12. Segment(E, F) → j
  13. OrthogonalLine(C, j) → k
  14. Intersect(k, j) → G
  15. Segment(C, G) → l
  16. Intersect(g, i) → H
  17. Intersect(g, h) → I
  18. Segment(H, E) → m
  19. Segment(I, F) → n
  20. Angle(C, G, F) → α
  21. Angle(C, H, E) → β
  22. Intersect(h, q) → J
  23. Circle(J, n) → r
  24. Intersect(r, h, 2) → K
  25. Circle(K, m) → s
  26. Intersect(s, h, 2) → L
  27. Semicircle(J, L) → t
  28. OrthogonalLine(K, h) → b
  29. Intersect(t, b, 1) → M
  30. Distance(M, K) → distanceMK
  31. Segment(A, C) → f_1
  32. Angle(I, C, A) → δ
  33. Circle(I, 1) → c_1
  34. Intersect(c_1, g, 2) → N
  35. Angle(N, I, F) → γ
  36. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'
  37. Segment(A, A') → g_1
  38. Dilate(E, If[1 < o ≤ 2, 2 - o, 0], H) → E'
  39. Segment(E, E') → h_1
  40. Dilate(F, If[2 < o ≤ 3, 3 - o, 0], I) → F'
  41. Segment(F, F') → i_1
  42. Dilate(E, If[3 < o ≤ 4, 4 - o, 0], F) → E'_1
  43. Segment(E, E'_1) → j_1
  44. Dilate(C, If[4 < o ≤ 5, 5 - o, 0], G) → C'
  45. Segment(C, C') → k_1
  46. Dilate(F, If[5 < o ≤ 6, 6 - o, 0], J) → F'_1
  47. Segment(F, F'_1) → l_1
  48. Dilate(J, If[6 < o ≤ 7, 7 - o, 0], K) → J'
  49. Segment(J, J') → m_1
  50. Dilate(K, If[7 < o ≤ 8, 8 - o, 0], L) → K'
  51. Segment(K, K') → n_1
  52. Rotate(F, If[8 < o ≤ 9, ((o - 8) * π / 2), π / 2], F) → F'_2
  53. Rotate(F', If[8 < o ≤ 9, ((o - 8) * π / 2), π / 2], F) → F''
  54. Segment(F'_2, F'') → p_1
  55. Dilate(F, If[9 < o ≤ 10, 10 - o, 0], J) → F'_3
  56. Vector(F, F'_3) → u
  57. Translate(F'_2, u) → O
  58. Translate(F'', u) → F'''
  59. Segment(O, F''') → q_1
  60. Rotate(O, If[10 < o ≤ 11, ((o - 10) * π / 2), π / 2], J) → O'
  61. Rotate(F''', If[10 < o ≤ 11, ((o - 10) * π / 2), π / 2], J) → P
  62. Segment(O', P) → r_1
  63. Dilate(H, If[11 < o ≤ 12, 12 - o, 0], K) → H'
  64. Vector(H, H') → v
  65. Translate(E, v) → E'_2
  66. Translate(E', v) → E''
  67. Segment(E'_2, E'') → s_1
  68. Midpoint(J, L) → Q
  69. Angle(L, Q, M) → ε
  70. Rotate(L, If[12 < o ≤ 13, ((o - 12) * ε), ε], Q) → L'
  71. CircleArc(Q, L, L') → d_1
  72. Rotate(M, If[13 < o ≤ 14, ((o - 13) * (π - ε)), π - ε], Q) → M'
  73. CircleArc(Q, M, M') → e_1
  74. CircleSector(Q, L, L') → t_1
  75. CircleSector(Q, M, M') → c_2
  76. CircleSector(Q, L, J) → d_2
  77. Angle(M, K, J) → ζ
  78. Dilate(M, If[14 < o ≤ 15, 15 - o, 0], K) → M'_1
  79. Segment(M, M'_1) → a_1
  80. Dilate(G, If[15 < o ≤ 16, 16 - o, 0], M) → G'
  81. Vector(G, G') → w
  82. Translate(C, w) → C'_1
  83. Translate(C', w) → C''
  84. Segment(C'_1, C'') → b_1
  85. Line(M, k_1) → f_2
  86. Intersect(f_2, g) → R
  87. Angle(R, M, K) → η
  88. Rotate(C'_1, If[16 < o ≤ 17, ((o - 16) * η), η], M) → S
  89. Rotate(C'', If[16 < o ≤ 17, ((o - 16) * η), η], M) → C'''
  90. Segment(S, C''') → g_2