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四边形的秘密

四边形的秘密
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2016-09-24 09:41
多边形角变换
这个范例展示了四边形的一个有趣但不常见的性质。它涉及四边形的角度和旋转等核心几何概念。通过使用GeoGebra中的Polygon, Angle, Rotate, Ray, Intersect等命令，可以动态地探索四边形的性质。适合初中及以上学生或教师使用，帮助理解几何变换和四边形的性质。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Angle(B, A, D) → α
  3. Angle(A, D, C) → β
  4. Angle(D, C, B) → γ
  5. Angle(C, B, A) → δ
  6. Rotate(B, α / 2, A) → B'
  7. Angle(B, A, B') → ε
  8. Ray(A, B') → f
  9. Rotate(A, β / 2, D) → A'
  10. Angle(A, D, A') → ζ
  11. Ray(D, A') → g
  12. Rotate(D, γ / 2, C) → D'
  13. Angle(D, C, D') → η
  14. Ray(C, D') → h
  15. Rotate(C, δ / 2, B) → C'
  16. Angle(C, B, C') → θ
  17. Ray(B, C') → i
  18. Intersect(h, i) → F
  19. Intersect(f, i) → E
  20. Intersect(f, g) → H
  21. Intersect(g, h) → G
  22. Circle(G, F, E) → e
  23. Line(E, G) → j
  24. Line(H, F) → k
  25. Midpoint(D, C) → I
  26. Midpoint(B, C) → J
  27. Midpoint(A, B) → K
  28. Midpoint(A, D) → L
  29. Line(D, C) → l
  30. Line(C, B) → m
  31. Line(B, A) → n
  32. Line(A, D) → p
  33. Intersect(p, m) → M
  34. Intersect(n, l) → N
  35. Min({a, b, c, d}) → o
  36. Circle(A, (0.25 * o)) → r
  37. Circle(B, (0.25 * o)) → q
  38. Circle(D, (0.25 * o)) → s
  39. Circle(C, (0.25 * o)) → t
  40. Intersect(q, m, 1) → O
  41. Intersect(q, i, 1) → P
  42. Intersect(r, n, 1) → Q
  43. Intersect(r, f, 1) → R
  44. Intersect(s, p, 1) → S
  45. Intersect(s, g, 1) → T
  46. Intersect(t, l, 1) → U
  47. Intersect(t, h, 1) → V
  48. CircleSector(A, Q, R) → c_1
  49. CircleSector(C, U, V) → d_1
  50. CircleSector(B, O, P) → e_1
  51. CircleSector(D, S, T) → f_1
  52. Dilate(B, If[0 < u ≤ 1, 1 - u, 0], F) → B'_1
  53. Dilate(C, If[0 < u ≤ 1, 1 - u, 0], F) → C'_1
  54. Segment(B, B'_1) → g_1
  55. Segment(C, C'_1) → h_1
  56. Dilate(D, If[1 < u ≤ 2, 2 - u, 0], H) → D'_1
  57. Segment(D, D'_1) → i_1
  58. Dilate(A, If[1 < u ≤ 2, 2 - u, 0], H) → A'_1
  59. Segment(A, A'_1) → j_1
  60. Rotate(e_1, If[2 < u ≤ 3, ((u - 2) * θ), θ], B) → k_1
  61. Rotate(d_1, If[3 < u ≤ 4, ((u - 3) * η), η], C) → p_1
  62. Rotate(f_1, If[4 < u ≤ 5, ((u - 4) * ζ), ζ], D) → q_1
  63. Rotate(c_1, If[5 < u ≤ 6, ((u - 5) * ε), ε], A) → r_1
  64. Center(e) → W
  65. Rotate(E, If[7.5 < u ≤ 8.5, (((u - 7.5) * 2) * π), (2 * π)], W) → E'
  66. CircleArc(W, E, E') → s_1