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莫利定理动态演示

莫利定理动态演示
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2016-09-10 10:57
测试改名0角几何作图
所属专题 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry Review Triangle Theorems
①本范例动态演示莫利定理，即任意三角形三个顶角三等分线的交点构成一个等边三角形；②涉及核心数学概念包括角、等边三角形、几何作图；③作图要点提炼自构造摘要，使用了Line（线段）、PointIn（点在对象上）、Polygon（多边形）、Angle（角度）、Rotate（旋转）、Ray（射线）、Intersect（交点）、Segment（线段）、Min（最小值）、Circle（圆）、CircleSector（圆扇形）、Dilate（缩放）等GeoGebra命令和对象；④适合高中及以上数学学习者，用于理解几何定理的动态证明和作图过程。

GeoGebra 命令及参数

  1. Line(A, B) → p
  2. PointIn(d) → C
  3. Polygon(A, B, C) → poly1, c, a, b
  4. Angle(poly1) → α, β, γ
  5. Rotate(B, α / 3, A) → B'
  6. Angle(B, A, B') → δ
  7. Ray(A, B') → f
  8. Rotate(B', α / 3, A) → B''
  9. Angle(B', A, B'') → ε
  10. Ray(A, B'') → g
  11. Rotate(C, β / 3, B) → C'
  12. Angle(C, B, C') → ζ
  13. Ray(B, C') → h
  14. Rotate(C', β / 3, B) → C''
  15. Angle(C', B, C'') → η
  16. Ray(B, C'') → i
  17. Rotate(A, γ / 3, C) → A'
  18. Angle(A, C, A') → θ
  19. Ray(C, A') → j
  20. Rotate(A', γ / 3, C) → A''
  21. Angle(A', C, A'') → ι
  22. Ray(C, A'') → k
  23. Intersect(f, i) → D
  24. Intersect(h, k) → E
  25. Intersect(g, j) → F
  26. Segment(D, E) → l
  27. Segment(E, F) → m
  28. Segment(F, D) → n
  29. Line(A, C) → q
  30. Line(C, B) → r
  31. Min({a, b, c}) → s
  32. Segment(A, B) → t
  33. Segment(B, C) → f_1
  34. Segment(C, A) → g_1
  35. Intersect(g, f_1) → G
  36. Intersect(f, f_1) → H
  37. Intersect(g_1, h) → I
  38. Intersect(g_1, i) → J
  39. Intersect(k, t) → K
  40. Intersect(j, t) → L
  41. Circle(A, (0.2 * s)) → c_1
  42. Circle(B, (0.2 * s)) → d_1
  43. Circle(C, (0.2 * s)) → e_1
  44. Intersect(d_1, f_1, 1) → M
  45. Intersect(d_1, h) → N,
  46. Intersect(c_1, f, 1) → O
  47. Intersect(c_1, t, 1) → P
  48. Intersect(e_1, g_1, 1) → Q
  49. Intersect(e_1, j, 1) → R
  50. CircleSector(B, M, N) → h_1
  51. CircleSector(A, P, O) → k_1
  52. CircleSector(C, Q, R) → p_1
  53. Polygon(D, E, F) → poly2, f_2, d_2, e_2
  54. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], D) → A'_1
  55. Dilate(B, If[0 < u ≤ 1, 1 - u, 0], E) → B'_1
  56. Dilate(C, If[0 < u ≤ 1, 1 - u, 0], F) → C'_1
  57. Segment(A, A'_1) → i_1
  58. Segment(B, B'_1) → j_1
  59. Segment(C, C'_1) → l_1
  60. Dilate(A, If[1 < u ≤ 2, 2 - u, 0], F) → A'_2
  61. Dilate(B, If[1 < u ≤ 2, 2 - u, 0], D) → B'_2
  62. Dilate(C, If[1 < u ≤ 2, 2 - u, 0], E) → C'_2
  63. Segment(A, A'_2) → m_1
  64. Segment(C, C'_2) → n_1
  65. Segment(B, B'_2) → q_1
  66. Rotate(k_1, If[2 < u ≤ 3, (((u - 2) * 2) * α / 3), (2 * α / 3)], A) → r_1
  67. Rotate(r_1, If[3.5 < u ≤ 4.5, ((-(u - 3.5)) * α / 3), ((-α)) / 3], A) → s_1
  68. Rotate(h_1, If[4.5 < u ≤ 5.5, (((u - 4.5) * 2) * β / 3), (2 * β / 3)], B) → t_1
  69. Rotate(t_1, If[6 < u ≤ 7, ((-(u - 6)) * β / 3), ((-β)) / 3], B) → c_2
  70. Rotate(p_1, If[7 < u ≤ 8, (((u - 7) * 2) * γ / 3), (2 * γ / 3)], C) → g_2
  71. Rotate(g_2, If[8.5 < u ≤ 9.5, ((-(u - 8.5)) * γ / 3), ((-γ)) / 3], C) → h_2
  72. Dilate(D, If[11 < u ≤ 12, 12 - u, 0], E) → D'
  73. Segment(D, D') → a_1
  74. Rotate(D, If[12 < u ≤ 13, ((u - 12) * π / 3), π / 3], D) → D'_1
  75. Rotate(D', If[12 < u ≤ 13, ((u - 12) * π / 3), π / 3], D) → D''
  76. Segment(D'_1, D'') → b_1
  77. Rotate(D'_1, If[13 < u ≤ 14, ((u - 13) * π / 3), π / 3], F) → S
  78. Rotate(D'', If[13 < u ≤ 14, ((u - 13) * π / 3), π / 3], F) → D'''
  79. Segment(S, D''') → i_2