积极 AI Logo 积极 AI

动态演示：亚历山大·波戈莫洛夫提出的问题

动态演示：亚历山大·波戈莫洛夫提出的问题
几何画板及绘图内容加载中，请稍等……
2017-02-11 05:55
角变换几何作图
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
这是一个动态可修改的几何图形，演示了亚历山大·波戈莫洛夫在Cut-the-Knot.org网站上提出的问题。该范例涉及角度、直线、四边形、等腰三角形等核心数学概念。通过使用GeoGebra命令如Segment、Circle、Line、Intersect等，可以构造出复杂的几何图形。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Segment(A, D) → f
  2. Circle(C, f) → e
  3. Line(C, D) → m
  4. Intersect(e, m) → H, I
  5. CircleArc(C, I, H) → p
  6. Point(p) → B
  7. Line(D, B) → g_1
  8. Segment(B, D) → n
  9. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], D) → A'
  10. Segment(A, A') → s
  11. Line(C, s) → c
  12. Segment(D, C) → g
  13. Midpoint(g) → N
  14. Segment(C, B) → h
  15. Segment(B, A) → i
  16. Midpoint(i) → M
  17. Segment(N, M) → j
  18. Segment(A, C) → k
  19. Intersect(k, n) → L
  20. Line(B, f) → l
  21. Line(A, h) → q
  22. Intersect(l, q) → K
  23. Segment(L, K) → r
  24. Slope(j) → m_1
  25. Slope(r) → m_2
  26. Dilate(D, If[1 < a ≤ 2, 2 - a, 0], N) → B'
  27. Segment(D, B') → t
  28. Dilate(N, If[2 < a ≤ 3, 3 - a, 0], C) → F'
  29. Segment(N, F') → b
  30. Rotate(D, If[3 < a ≤ 4, ((a - 3) * π), π], N) → B'_1
  31. Rotate(B', If[3 < a ≤ 4, ((a - 3) * π), π], N) → B''
  32. Intersect(g_1, c) → M_1
  33. Angle(M_1, C, B) → α
  34. Segment(B'_1, B'') → t'
  35. Dilate(D, If[4 < a ≤ 5, 5 - a, 0], C) → B'_2
  36. Vector(D, B'_2) → u
  37. Translate(A, u) → A'_1
  38. Translate(A', u) → A''
  39. Segment(A'_1, A'') → s'
  40. Rotate(A'_1, If[5 < a ≤ 6, ((a - 5) * α), α], C) → K_1
  41. Rotate(A'', If[5 < a ≤ 6, ((a - 5) * α), α], C) → A'''
  42. Segment(K_1, A''') → s''
  43. Dilate(A, If[6 < a ≤ 7, 7 - a, 0], M) → A'_2
  44. Segment(A, A'_2) → d
  45. Dilate(M, If[7 < a ≤ 8, 8 - a, 0], B) → E'
  46. Segment(M, E') → f_1
  47. Rotate(A, If[8 < a ≤ 9, ((a - 8) * π), π], M) → A'_3
  48. Rotate(A'_2, If[8 < a ≤ 9, ((a - 8) * π), π], M) → L_1
  49. Segment(A'_3, L_1) → d'
  50. Polygon(A, D, C, B) → poly1, a_1, b_1, c_1, d_1
  51. Dilate(N, If[9 < a ≤ 10, 10 - a, 0], M) → F'_1
  52. Segment(N, F'_1) → h_1
  53. Circle(C, 5) → e_1
  54. Intersect(e_1, m, 1) → N_1
  55. Ray(C, N_1) → i_1
  56. Intersect(m, q) → O
  57. Segment(D, O) → j_1
  58. Segment(O, N) → k_1
  59. Min(j_1, k_1) → o
  60. Circle(C, (0.25 * o)) → p_1
  61. Intersect(p_1, i_1, 1) → P
  62. Intersect(p_1, s'', 1) → Q
  63. Angle(Q, C, P) → β
  64. Rotate(Q, If[10 < a ≤ 11, ((a - 10) * β), β], C) → Q'
  65. CircleSector(C, Q, Q') → q_1
  66. Dilate(A, If[11 < a ≤ 12, 12 - a, 0], K) → A'_4
  67. Segment(A, A'_4) → l_1
  68. Dilate(C, If[12 < a ≤ 13, 13 - a, 0], O) → C'
  69. Vector(C, C') → v
  70. Translate(q_1, v) → r_1
  71. Intersect(m, l) → R
  72. Line(D, A) → n_1
  73. Circle(D, 5) → s_1
  74. Intersect(s_1, n_1, 1) → S
  75. Ray(D, S) → t_1
  76. Segment(N, R) → f_2
  77. Segment(R, C) → g_2
  78. Min(f_2, g_2) → w
  79. Circle(D, (0.25 * w)) → c_2
  80. Intersect(c_2, t_1, 1) → U
  81. Intersect(c_2, m) → T, V
  82. Angle(T, D, U) → γ
  83. Rotate(T, If[13 < a ≤ 14, ((a - 13) * γ), γ], D) → T'
  84. CircleSector(D, T, T') → d_2
  85. Dilate(D, If[15 < a ≤ 16, 16 - a, 0], R) → B'_3
  86. Vector(D, B'_3) → u_1
  87. Translate(d_2, u_1) → e_2
  88. Dilate(B, If[14 < a ≤ 15, 15 - a, 0], K) → D'
  89. Segment(B, D') → h_2
  90. Intersect(m, r) → W
  91. Circle(W, (0.6 * Distance[W, N])) → k_2
  92. Dilate(A, If[16 < a ≤ 17, 17 - a, 0], L) → A'_5
  93. Dilate(B, If[16 < a ≤ 17, 17 - a, 0], L) → D'_1
  94. Segment(A, A'_5) → i_2
  95. Segment(B, D'_1) → j_2
  96. Line(K, W) → l_2
  97. Intersect(k_2, l_2) → Z, A_1
  98. Intersect(k_2, m) → B_1, C_1
  99. Dilate(L, If[17 < a ≤ 18, 18 - a, 0], D) → G'
  100. Dilate(L, If[17 < a ≤ 18, 18 - a, 0], C) → G'_1
  101. Segment(L, G') → n_2
  102. Segment(L, G'_1) → p_2
  103. Dilate(L, If[18 < a ≤ 19, 19 - a, 0], K) → G'_2
  104. Segment(L, G'_2) → q_2
  105. Angle(A_1, W, B_1) → δ
  106. Rotate(A_1, If[19 < a ≤ 20, ((a - 19) * δ), δ], W) → D_1
  107. CircleSector(W, A_1, D_1) → r_2
  108. Dilate(W, If[20 < a ≤ 21, 21 - a, 0], N) → W'
  109. Vector(W, W') → v_1
  110. Translate(r_2, v_1) → s_2