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动画258：等边三角形内切圆

动画258：等边三角形内切圆
几何画板及绘图内容加载中，请稍等……
2017-05-15 09:21
测试改名0圆多边形几何作图滑块动画
这个范例演示了等边三角形的内切圆。涉及的核心数学概念包括三角形、内切圆和等边三角形。通过使用GeoGebra命令如Polygon、Centroid、Tangent和Dilate等，可以构造出等边三角形及其内切圆。适合初中和高中学生学习几何作图和内切圆的相关知识。

GeoGebra 命令及参数

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. Segment(A, B) → i
  3. Segment(B, C) → j
  4. Segment(C, A) → k
  5. Centroid(poly1) → D
  6. OrthogonalLine(D, g) → l
  7. OrthogonalLine(D, i) → m
  8. Intersect(l, g) → E
  9. Circle(D, E) → c
  10. Angle(B, A, C) → α
  11. Rotate(B, 30°, A) → B'
  12. Angle(B, A, B') → β
  13. Line(A, B') → n
  14. Intersect(c, n, 1) → F
  15. Midpoint(A, F) → G
  16. Tangent(F, c) → p,
  17. Intersect(p, i) → H
  18. Intersect(p, h) → I
  19. Polygon(A, H, I) → poly2, i_1, a, h_1
  20. Centroid(poly2) → J
  21. Circle(J, F) → d
  22. Intersect(c, m, 2) → K
  23. Tangent(K, c) → q,
  24. Intersect(q, g) → L
  25. Intersect(q, h) → M
  26. Polygon(M, L, C) → poly3, c_1, m_1, l_1
  27. Centroid(poly3) → N
  28. Line(B, D) → r
  29. Intersect(h, k) → O
  30. Intersect(r, h) → P
  31. Intersect(c, r) → Q, R
  32. Tangent(Q, c) → s,
  33. Intersect(s, g) → S
  34. Intersect(s, i) → T
  35. Polygon(T, B, S) → poly4, s_1, t, b
  36. Centroid(poly4) → U
  37. Circle(U, Q) → d_1
  38. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  39. Segment(A, A') → a_1
  40. Rotate(A, If[1 < o ≤ 2, ((o - 1) * π / 3), π / 3], A) → A'_1
  41. Rotate(A', If[1 < o ≤ 2, ((o - 1) * π / 3), π / 3], A) → A''
  42. Segment(A'_1, A'') → b_1
  43. Rotate(A, If[2 < o ≤ 3, ((-(o - 2)) * π / 3), ((-π)) / 3], B) → A'_2
  44. Rotate(A', If[2 < o ≤ 3, ((-(o - 2)) * π / 3), ((-π)) / 3], B) → A''_1
  45. Segment(A'_2, A''_1) → e_1
  46. Intersect(d, dd, 1) → W_1
  47. Intersect(dd, a_1) → Z_1, A_1
  48. Intersect(ddd, a_1) → A_2, B_1
  49. Center(cc) → B_2
  50. OrthogonalLine(B_2, e_1) → k_3
  51. Intersect(k_3, e_1) → C_2
  52. Angle(B_2, C_2, B) → ι
  53. Tangent(C_2, dd) → l_3, m_3
  54. Intersect(dd, l_3) → V
  55. Center(dd) → C_1
  56. Center(ddd) → D_1
  57. Dilate(B_2, If[3.5 < o ≤ 4.5, 4.5 - o, 0], C_2) → E_1
  58. Dilate(C_1, If[3.5 < o ≤ 4.5, 4.5 - o, 0], A_1) → F_1
  59. Dilate(D_1, If[3.5 < o ≤ 4.5, 4.5 - o, 0], A_2) → G_1
  60. Segment(B_2, E_1) → f_1
  61. Segment(D_1, G_1) → g_1
  62. Segment(C_1, F_1) → j_1
  63. Angle(C_1, V, C_2) → δ
  64. OrthogonalLine(C_1, a_1) → k_1
  65. Intersect(k_1, a_1) → H_1
  66. Angle(C_1, H_1, A) → γ
  67. OrthogonalLine(D_1, a_1) → n_1
  68. Intersect(n_1, a_1) → I_1
  69. Angle(B, I_1, D_1) → ε
  70. Dilate(C_1, If[4.5 < o ≤ 5.5, 5.5 - o, 0], V) → K_1
  71. Segment(C_1, K_1) → p_1
  72. Dilate(C_2, If[5.5 < o ≤ 6.5, 6.5 - o, 0], V) → L_1
  73. Segment(C_2, L_1) → q_1
  74. Dilate(H_1, If[5.5 < o ≤ 6.5, 6.5 - o, 0], I_1) → M_1
  75. Dilate(V, If[6.5 < o ≤ 7.5, 7.5 - o, 0], C_1) → V'
  76. Vector(V, V') → u
  77. Translate(C_2, u) → W
  78. Translate(L_1, u) → Z
  79. Segment(W, Z) → e
  80. Line(A, B) → r_1
  81. Line(V, r_1) → t_1
  82. Point(t_1) → N_1
  83. Angle(N_1, V, C_2) → ζ
  84. Rotate(W, If[7.5 < o ≤ 8.5, ((-(o - 7.5)) * ζ), (-ζ)], C_1) → W'
  85. Rotate(Z, If[7.5 < o ≤ 8.5, ((-(o - 7.5)) * ζ), (-ζ)], C_1) → Z'
  86. Segment(W', Z') → e'