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动画演示多边形与圆的关系

动画演示多边形与圆的关系
几何画板及绘图内容加载中，请稍等……
2017-05-02 23:23
圆多边形几何作图
①本范例通过动画演示了多边形的外接圆与内切圆的构造与性质；②涉及核心数学概念包括外接圆、内切圆、多边形、角度、向量等；③作图要点提炼自构造摘要，使用了 Rotate（旋转）、Circle（圆）、Intersect（交点）、Polygon（多边形）等 GeoGebra 命令与对象；④适合高中及以上数学学习者，用于理解多边形与圆的几何关系及动画制作。

GeoGebra 命令及参数

  1. Rotate(B_2, (a * π / 180), A) → B'
  2. Ray(A, B') → g
  3. Point(g) → B
  4. Segment(A, B) → j
  5. Ray(A, B_2) → f
  6. Point(f) → C
  7. Segment(B, C) → h
  8. Segment(A, C) → i
  9. Min({i, j, h}) → b
  10. Angle(B_2, A, B') → α
  11. Circle(C, (0.2 * b)) → d
  12. Circle(B, 4) → c
  13. Intersect(c, g, 2) → E_2
  14. Intersect(d, f, 2) → F_2
  15. Ray(C, F_2) → k
  16. Ray(B, E_2) → l
  17. Circle(B, (0.2 * b)) → e
  18. Circle(C, (0.15 * b)) → p
  19. Angle(F_2, C, B) → β
  20. Angle(C, B, E_2) → γ
  21. Rotate(F_2, β / 2, C) → F'
  22. Angle(F_2, C, F') → δ
  23. Rotate(C, γ / 2, B) → D'
  24. Angle(C, B, D') → ε
  25. Ray(B, D') → m
  26. Ray(C, F') → n
  27. Intersect(e, m, 1) → G_2
  28. Intersect(e, h, 1) → H_2
  29. Intersect(p, h, 1) → I
  30. Polygon(A, C, B) → poly1, c_2, a_1, d_2
  31. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'
  32. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'_1
  33. Segment(A, A') → k_1
  34. Segment(A, A'_1) → l_1
  35. Min(c_2, d_2) → w
  36. Circle(A, (0.15 * w)) → e_2
  37. Segment(A, B) → m_2
  38. Intersect(e_2, m_2) → S,
  39. Segment(A, C) → n_2
  40. Intersect(e_2, n_2) → T,
  41. Min({h, k_1, l_1}) → b_1
  42. Intersect(d, h, 1) → U
  43. Intersect(e, h) → W,
  44. Angle(A, B, C) → λ
  45. Angle(B, C, A) → κ
  46. Rotate(A, λ / 2, B) → A'_2
  47. Angle(A, B, A'_2) → ι
  48. Ray(B, A'_2) → t_1
  49. Rotate(B, κ / 2, C) → C'_1
  50. Angle(B, C, C'_1) → μ_1
  51. Ray(C, C'_1) → f_2
  52. Intersect(d, f_2) → A_1,
  53. CircleSector(C, U, A_1) → r_2
  54. Intersect(t_1, f_2) → O
  55. OrthogonalLine(O, k_1) → s_2
  56. OrthogonalLine(O, l_1) → t_2
  57. Intersect(s_2, k_1) → E
  58. Intersect(t_2, l_1) → F
  59. Intersect(k_1, t_1) → D_1
  60. Circle(A, (0.2 * b)) → q_2
  61. Angle(C, A, B) → μ
  62. Rotate(C, μ / 2, A) → D'_2
  63. Angle(C, A, D'_2) → ν
  64. Ray(A, D'_2) → a_2
  65. Intersect(q_2, a_2) → V,
  66. Intersect(q_2, k_1) → E_1,
  67. CircleSector(A, E_1, V) → p_2
  68. Dilate(C, If[1 < o ≤ 2, 2 - o, 0], O) → D'_3
  69. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], O) → A'_3
  70. Segment(A, A'_3) → b_2
  71. Segment(C, D'_3) → f_3
  72. Rotate(r_2, If[2.5 < o ≤ 3.5, ((o - 2.5) * κ / 2), κ / 2], C) → c_3
  73. Rotate(p_2, If[3.5 < o ≤ 4.5, ((o - 3.5) * μ / 2), μ / 2], A) → d_3
  74. Dilate(O, If[5 < o ≤ 6, 6 - o, 0], F) → Z'
  75. Dilate(O, If[5 < o ≤ 6, 6 - o, 0], E) → Z'_1
  76. Segment(O, Z') → g_3
  77. Segment(O, Z'_1) → h_3
  78. Angle(O, E, A) → ξ
  79. Angle(A, F, O) → ο
  80. Circle(O, Z') → e_3
  81. Rotate(F, If[6 < o ≤ 9, (((o - 6) * 2) * π / 3), (2 * π)], O) → F_1
  82. Segment(B, D_1) → i_3
  83. Intersect(e, i_3) → G_1,
  84. Intersect(e, l_1) → H_1,
  85. Dilate(B, If[9.5 < o ≤ 10.5, 10.5 - o, 0], O) → C'_2
  86. Polygon(A, O, B) → poly2, c_4, a_3, z_1
  87. CircleArc(O, Z', F_1) → k_3
  88. OrthogonalLine(O, h) → q
  89. Intersect(q, h) → D
  90. Line(A, O) → r
  91. Line(F, D) → s
  92. Intersect(r, s) → H
  93. Line(C, O) → t
  94. Intersect(s, t) → G
  95. Dilate(O, If[5 < o ≤ 6, 6 - o, 0], D) → O'
  96. Segment(O, O') → f_1
  97. Angle(O, D, C) → ζ
  98. Circle(A, G, F) → c_1
  99. Circle(C, H, D) → d_1
  100. Ray(D, H) → g_1
  101. Ray(F, G) → h_1
  102. Dilate(F, If[9 < o ≤ 10, 10 - o, 0], D) → F'_1
  103. Segment(F, F'_1) → i_1
  104. Dilate(O, If[10 < o ≤ 11, 11 - o, 0], H) → O'_1
  105. Segment(O, O'_1) → j_1
  106. Dilate(O, If[10 < o ≤ 11, 11 - o, 0], G) → O'_2
  107. Segment(O, O'_2) → m_1
  108. Center(c_1) → J
  109. Rotate(F, If[11 < o ≤ 13, ((o - 11) * π), (2 * π)], J) → F'_2
  110. CircleArc(J, F, F'_2) → e_1
  111. Center(d_1) → K
  112. Rotate(D, If[13 < o ≤ 15, ((o - 13) * π), (2 * π)], K) → D'_1
  113. CircleArc(K, D, D'_1) → p_1
  114. Dilate(E, If[15 < o ≤ 16, 16 - o, 0], H) → F'_3
  115. Dilate(E, If[15 < o ≤ 16, 16 - o, 0], G) → E'
  116. Segment(E, F'_3) → n_1
  117. Segment(E, J) → q_1
  118. Segment(E, E') → r_1
  119. Angle(G, H, E) → τ
  120. Angle(H, G, E) → θ
  121. Line(A, h_1) → s_1
  122. Intersect(d_1, s_1, 1) → L
  123. Line(B, A) → g_2
  124. Point(g_2) → M
  125. Polygon(E, H, G) → poly3, g_4, e_4, h_2
  126. Angle(L, A, B) → ρ
  127. Dilate(A, If[16 < o ≤ 17, 17 - o, 0], G) → A'_4
  128. Vector(A, A'_4) → u
  129. Translate(d_3, u) → k_2
  130. Rotate(k_2, If[17 < o ≤ 18, ((-(o - 17)) * ρ), (-ρ)], G) → p_3
  131. Midpoint(A, G) → N
  132. Dilate(A, If[18 < o ≤ 19, 19 - o, 0], N) → A'_5
  133. Vector(A, A'_5) → v
  134. Translate(d_3, v) → q_3
  135. Rotate(q_3, If[19 < o ≤ 20, ((-(o - 19)) * (ρ + θ / 2)), (-(ρ + θ / 2))], N) → r_3
  136. Dilate(N, If[20 < o ≤ 21, 21 - o, 0], G) → N'
  137. Vector(N, N') → u_1
  138. Translate(r_3, u_1) → s_3
  139. Line(C, g_1) → i_2
  140. Intersect(d_1, i_2, 2) → P
  141. Midpoint(C, H) → Q
  142. Angle(O, C, P) → σ
  143. Dilate(C, If[21 < o ≤ 22, 22 - o, 0], H) → C'
  144. Vector(C, C') → v_1
  145. Translate(c_3, v_1) → t_3
  146. Rotate(t_3, If[22 < o ≤ 23, ((o - 22) * σ), σ], H) → d_4
  147. Dilate(C, If[23 < o ≤ 24, 24 - o, 0], Q) → C'_3
  148. Vector(C, C'_3) → w_1
  149. Translate(c_3, w_1) → f_4
  150. Rotate(f_4, If[24 < o ≤ 25, ((o - 24) * (σ + τ / 2)), σ + τ / 2], Q) → h_4
  151. Dilate(Q, If[25 < o ≤ 26, 26 - o, 0], H) → Q'
  152. Vector(Q, Q') → u_2
  153. Translate(h_4, u_2) → k_4
  154. Circle(A, G, H) → p_4
  155. Center(p_4) → R
  156. Rotate(H, If[26 < o ≤ 28, ((o - 26) * π), (2 * π)], R) → H'
  157. CircleArc(R, H, H') → q_4
  158. Distance(A, R) → distanceAR
  159. Distance(R, C) → distanceRC