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埃拉托斯特尼筛法

埃拉托斯特尼筛法
几何画板及绘图内容加载中，请稍等……
2016-05-04 21:50
数列解析几何几何作图
所属专题 Arithmetic Operations (preGED)
①本范例动态演示了埃拉托斯特尼筛法寻找小于给定自然数的所有质数的过程；②涉及核心数学概念：质数判定、筛选算法、自然数集合；③作图要点：运用了Polygon（多边形）、Point（点）、Rotate（旋转）、Circle（圆）、Segment（线段）、Intersect（交点）、Sequence（序列）、Union（并集）、RemoveUndefined（移除未定义对象）等GeoGebra命令与对象；④适合初中及以上数学学习者，用于理解质数分布规律及算法实现。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → a1, f, g, h, i, C, D
  2. Point(Circle[E, Segment[A, B]]) → F
  3. Rotate(F + (Segment[B, C], 0), Angle[C - B] + Angle[F - E] - Angle[B - A], F) → G
  4. Rotate(G + (Segment[C, D], 0), Angle[D - C] + Angle[G - F] - Angle[C - B], G) → H
  5. Polygon(E, F, G, H) → a2, e, f_1, g_1, h_1
  6. Point(Circle[I, Segment[E, F]]) → J
  7. Rotate(J + (Segment[F, G], 0), Angle[G - F] + Angle[J - I] - Angle[F - E], J) → K
  8. Rotate(K + (Segment[G, H], 0), Angle[H - G] + Angle[K - J] - Angle[G - F], K) → L
  9. Polygon(I, J, K, L) → a3, i_1, j, k, l
  10. Point(Circle[M, Segment[I, J]]) → N
  11. Rotate(N + (Segment[J, K], 0), Angle[K - J] + Angle[N - M] - Angle[J - I], N) → O
  12. Rotate(O + (Segment[K, L], 0), Angle[L - K] + Angle[O - N] - Angle[K - J], O) → P
  13. Polygon(M, N, O, P) → a4, m, n, o, p
  14. Point(Circle[Q, Segment[M, N]]) → R
  15. Rotate(R + (Segment[N, O], 0), Angle[O - N] + Angle[R - Q] - Angle[N - M], R) → S
  16. Rotate(S + (Segment[O, P], 0), Angle[P - O] + Angle[S - R] - Angle[O - N], S) → T
  17. Polygon(Q, R, S, T) → a5, q, r, s, t
  18. Point(Circle[U, Segment[Q, R]]) → V
  19. Rotate(V + (Segment[R, S], 0), Angle[S - R] + Angle[V - U] - Angle[R - Q], V) → W
  20. Rotate(W + (Segment[S, T], 0), Angle[T - S] + Angle[W - V] - Angle[S - R], W) → Z
  21. Polygon(U, V, W, Z) → a6, u, v, w, z_1
  22. Point(Circle[A_1, Segment[U, V]]) → B_1
  23. Rotate(B_1 + (Segment[V, W], 0), Angle[W - V] + Angle[B_1 - A_1] - Angle[V - U], B_1) → C_1
  24. Rotate(C_1 + (Segment[W, Z], 0), Angle[Z - W] + Angle[C_1 - B_1] - Angle[W - V], C_1) → D_1
  25. Polygon(A_1, B_1, C_1, D_1) → a7, a_1, b_1, c_1, d_1
  26. Point(Circle[E_1, Segment[A_1, B_1]]) → F_1
  27. Rotate(F_1 + (Segment[B_1, C_1], 0), Angle[C_1 - B_1] + Angle[F_1 - E_1] - Angle[B_1 - A_1], F_1) → G_1
  28. Rotate(G_1 + (Segment[C_1, D_1], 0), Angle[D_1 - C_1] + Angle[G_1 - F_1] - Angle[C_1 - B_1], G_1) → H_1
  29. Polygon(E_1, F_1, G_1, H_1) → a8, e_1, f_2, g_2, h_2
  30. Point(Circle[I_1, Segment[E_1, F_1]]) → J_1
  31. Rotate(J_1 + (Segment[F_1, G_1], 0), Angle[G_1 - F_1] + Angle[J_1 - I_1] - Angle[F_1 - E_1], J_1) → K_1
  32. Rotate(K_1 + (Segment[G_1, H_1], 0), Angle[H_1 - G_1] + Angle[K_1 - J_1] - Angle[G_1 - F_1], K_1) → L_1
  33. Polygon(I_1, J_1, K_1, L_1) → a9, i_2, j_1, k_1, l_1
  34. Point(Circle[M_1, Segment[I_1, J_1]]) → N_1
  35. Rotate(N_1 + (Segment[J_1, K_1], 0), Angle[K_1 - J_1] + Angle[N_1 - M_1] - Angle[J_1 - I_1], N_1) → O_1
  36. Rotate(O_1 + (Segment[K_1, L_1], 0), Angle[L_1 - K_1] + Angle[O_1 - N_1] - Angle[K_1 - J_1], O_1) → P_1
  37. Polygon(M_1, N_1, O_1, P_1) → a10, m_1, n_1, o_1, p_1
  38. Circle(Q_1, 0.3) → c
  39. Circle(R_1, 0.3) → d
  40. Circle(S_1, 0.3) → q_1
  41. Circle(T_1, 0.3) → r_1
  42. Circle(U_1, 0.3) → s_1
  43. Circle(V_1, 0.3) → t_1
  44. Circle((x(Q_1), y(Q_1)), 0.3) → c'
  45. Circle((x(R_1), y(R_1)), 0.3) → d'
  46. Circle((x(S_1), y(S_1)), 0.3) → q_1'
  47. Circle((x(T_1), y(T_1)), 0.3) → r_1'
  48. Circle((x(U_1), y(U_1)), 0.3) → s_1'
  49. Circle((x(V_1), y(V_1)), 0.3) → t_1'
  50. Point(Circle[W_1, Segment[A, B]]) → Z_1
  51. Rotate(Z_1 + (Segment[B, C], 0), Angle[C - B] + Angle[Z_1 - W_1] - Angle[B - A], Z_1) → A_2
  52. Rotate(A_2 + (Segment[C, D], 0), Angle[D - C] + Angle[A_2 - Z_1] - Angle[C - B], A_2) → B_2
  53. Polygon(W_1, Z_1, A_2, B_2) → a11, w_1, z_2, a_2, b_2
  54. Point(Circle[C_2, Segment[W_1, Z_1]]) → D_2
  55. Rotate(D_2 + (Segment[Z_1, A_2], 0), Angle[A_2 - Z_1] + Angle[D_2 - C_2] - Angle[Z_1 - W_1], D_2) → E_2
  56. Rotate(E_2 + (Segment[A_2, B_2], 0), Angle[B_2 - A_2] + Angle[E_2 - D_2] - Angle[A_2 - Z_1], E_2) → F_2
  57. Polygon(C_2, D_2, E_2, F_2) → a12, c_2, d_2, e_2, f_3
  58. Point(Circle[G_2, Segment[C_2, D_2]]) → H_2
  59. Rotate(H_2 + (Segment[D_2, E_2], 0), Angle[E_2 - D_2] + Angle[H_2 - G_2] - Angle[D_2 - C_2], H_2) → I_2
  60. Rotate(I_2 + (Segment[E_2, F_2], 0), Angle[F_2 - E_2] + Angle[I_2 - H_2] - Angle[E_2 - D_2], I_2) → J_2
  61. Polygon(G_2, H_2, I_2, J_2) → a13, g_3, h_3, i_3, j_2
  62. Point(Circle[K_2, Segment[G_2, H_2]]) → L_2
  63. Rotate(L_2 + (Segment[H_2, I_2], 0), Angle[I_2 - H_2] + Angle[L_2 - K_2] - Angle[H_2 - G_2], L_2) → M_2
  64. Rotate(M_2 + (Segment[I_2, J_2], 0), Angle[J_2 - I_2] + Angle[M_2 - L_2] - Angle[I_2 - H_2], M_2) → N_2
  65. Polygon(K_2, L_2, M_2, N_2) → a14, k_2, l_2, m_2, n_2
  66. Point(Circle[O_2, Segment[K_2, L_2]]) → P_2
  67. Rotate(P_2 + (Segment[L_2, M_2], 0), Angle[M_2 - L_2] + Angle[P_2 - O_2] - Angle[L_2 - K_2], P_2) → Q_2
  68. Rotate(Q_2 + (Segment[M_2, N_2], 0), Angle[N_2 - M_2] + Angle[Q_2 - P_2] - Angle[M_2 - L_2], Q_2) → R_2
  69. Polygon(O_2, P_2, Q_2, R_2) → a15, o_2, p_2, q_2, r_2
  70. Point(Circle[S_2, Segment[O_2, P_2]]) → T_2
  71. Rotate(T_2 + (Segment[P_2, Q_2], 0), Angle[Q_2 - P_2] + Angle[T_2 - S_2] - Angle[P_2 - O_2], T_2) → U_2
  72. Rotate(U_2 + (Segment[Q_2, R_2], 0), Angle[R_2 - Q_2] + Angle[U_2 - T_2] - Angle[Q_2 - P_2], U_2) → V_2
  73. Polygon(S_2, T_2, U_2, V_2) → a16, s_2, t_2, u_2, v_2
  74. Point(Circle[W_2, Segment[S_2, T_2]]) → Z_2
  75. Rotate(Z_2 + (Segment[T_2, U_2], 0), Angle[U_2 - T_2] + Angle[Z_2 - W_2] - Angle[T_2 - S_2], Z_2) → A_3
  76. Rotate(A_3 + (Segment[U_2, V_2], 0), Angle[V_2 - U_2] + Angle[A_3 - Z_2] - Angle[U_2 - T_2], A_3) → B_3
  77. Polygon(W_2, Z_2, A_3, B_3) → a17, w_2, z_3, a_3, b_3
  78. Point(Circle[C_3, Segment[W_2, Z_2]]) → D_3
  79. Rotate(D_3 + (Segment[Z_2, A_3], 0), Angle[A_3 - Z_2] + Angle[D_3 - C_3] - Angle[Z_2 - W_2], D_3) → E_3
  80. Rotate(E_3 + (Segment[A_3, B_3], 0), Angle[B_3 - A_3] + Angle[E_3 - D_3] - Angle[A_3 - Z_2], E_3) → F_3
  81. Polygon(C_3, D_3, E_3, F_3) → a18, c_3, d_3, e_3, f_4
  82. Point(Circle[G_3, Segment[C_3, D_3]]) → H_3
  83. Rotate(H_3 + (Segment[D_3, E_3], 0), Angle[E_3 - D_3] + Angle[H_3 - G_3] - Angle[D_3 - C_3], H_3) → I_3
  84. Rotate(I_3 + (Segment[E_3, F_3], 0), Angle[F_3 - E_3] + Angle[I_3 - H_3] - Angle[E_3 - D_3], I_3) → J_3
  85. Polygon(G_3, H_3, I_3, J_3) → a19, g_4, h_4, i_4, j_3
  86. Point(Circle[K_3, Segment[G_3, H_3]]) → L_3
  87. Rotate(L_3 + (Segment[H_3, I_3], 0), Angle[I_3 - H_3] + Angle[L_3 - K_3] - Angle[H_3 - G_3], L_3) → M_3
  88. Rotate(M_3 + (Segment[I_3, J_3], 0), Angle[J_3 - I_3] + Angle[M_3 - L_3] - Angle[I_3 - H_3], M_3) → N_3
  89. Polygon(K_3, L_3, M_3, N_3) → a20, k_3, l_3, m_3, n_3
  90. Polygon(A_6, B_6, 4) → a1_1, f_7, g_7, h_7, i_7, C_6, D_6
  91. Point(Circle[W_4, Segment[A_6, B_6]]) → Z_4
  92. Rotate(Z_4 + (Segment[B_6, C_6], 0), Angle[C_6 - B_6] + Angle[Z_4 - W_4] - Angle[B_6 - A_6], Z_4) → A_5
  93. Rotate(A_5 + (Segment[C_6, D_6], 0), Angle[D_6 - C_6] + Angle[A_5 - Z_4] - Angle[C_6 - B_6], A_5) → B_5
  94. Polygon(W_4, Z_4, A_5, B_5) → a21, w_4, z_5, a_5, b_5
  95. Point(Circle[C_5, Segment[W_4, Z_4]]) → D_5
  96. Rotate(D_5 + (Segment[Z_4, A_5], 0), Angle[A_5 - Z_4] + Angle[D_5 - C_5] - Angle[Z_4 - W_4], D_5) → E_5
  97. Rotate(E_5 + (Segment[A_5, B_5], 0), Angle[B_5 - A_5] + Angle[E_5 - D_5] - Angle[A_5 - Z_4], E_5) → F_5
  98. Polygon(C_5, D_5, E_5, F_5) → a22, c_5, d_5, e_5, f_6
  99. Point(Circle[G_5, Segment[C_5, D_5]]) → H_5
  100. Rotate(H_5 + (Segment[D_5, E_5], 0), Angle[E_5 - D_5] + Angle[H_5 - G_5] - Angle[D_5 - C_5], H_5) → I_5
  101. Rotate(I_5 + (Segment[E_5, F_5], 0), Angle[F_5 - E_5] + Angle[I_5 - H_5] - Angle[E_5 - D_5], I_5) → J_5
  102. Polygon(G_5, H_5, I_5, J_5) → a23, g_6, h_6, i_6, j_5
  103. Point(Circle[K_5, Segment[G_5, H_5]]) → L_5
  104. Rotate(L_5 + (Segment[H_5, I_5], 0), Angle[I_5 - H_5] + Angle[L_5 - K_5] - Angle[H_5 - G_5], L_5) → M_5
  105. Rotate(M_5 + (Segment[I_5, J_5], 0), Angle[J_5 - I_5] + Angle[M_5 - L_5] - Angle[I_5 - H_5], M_5) → N_5
  106. Polygon(K_5, L_5, M_5, N_5) → a24, k_5, l_5, m_5, n_5
  107. Point(Circle[O_3, Segment[K_5, L_5]]) → P_3
  108. Rotate(P_3 + (Segment[L_5, M_5], 0), Angle[M_5 - L_5] + Angle[P_3 - O_3] - Angle[L_5 - K_5], P_3) → Q_3
  109. Rotate(Q_3 + (Segment[M_5, N_5], 0), Angle[N_5 - M_5] + Angle[Q_3 - P_3] - Angle[M_5 - L_5], Q_3) → R_3
  110. Polygon(O_3, P_3, Q_3, R_3) → a25, o_3, p_3, q_3, r_3
  111. Point(Circle[S_3, Segment[O_3, P_3]]) → T_3
  112. Rotate(T_3 + (Segment[P_3, Q_3], 0), Angle[Q_3 - P_3] + Angle[T_3 - S_3] - Angle[P_3 - O_3], T_3) → U_3
  113. Rotate(U_3 + (Segment[Q_3, R_3], 0), Angle[R_3 - Q_3] + Angle[U_3 - T_3] - Angle[Q_3 - P_3], U_3) → V_3
  114. Polygon(S_3, T_3, U_3, V_3) → a26, s_3, t_3, u_1, v_1
  115. Point(Circle[W_3, Segment[S_3, T_3]]) → Z_3
  116. Rotate(Z_3 + (Segment[T_3, U_3], 0), Angle[U_3 - T_3] + Angle[Z_3 - W_3] - Angle[T_3 - S_3], Z_3) → A_4
  117. Rotate(A_4 + (Segment[U_3, V_3], 0), Angle[V_3 - U_3] + Angle[A_4 - Z_3] - Angle[U_3 - T_3], A_4) → B_4
  118. Polygon(W_3, Z_3, A_4, B_4) → a27, w_3, z_4, a_4, b_4
  119. Point(Circle[C_4, Segment[W_3, Z_3]]) → D_4
  120. Rotate(D_4 + (Segment[Z_3, A_4], 0), Angle[A_4 - Z_3] + Angle[D_4 - C_4] - Angle[Z_3 - W_3], D_4) → E_4
  121. Rotate(E_4 + (Segment[A_4, B_4], 0), Angle[B_4 - A_4] + Angle[E_4 - D_4] - Angle[A_4 - Z_3], E_4) → F_4
  122. Polygon(C_4, D_4, E_4, F_4) → a28, c_4, d_4, e_4, f_5
  123. Point(Circle[G_4, Segment[C_4, D_4]]) → H_4
  124. Rotate(H_4 + (Segment[D_4, E_4], 0), Angle[E_4 - D_4] + Angle[H_4 - G_4] - Angle[D_4 - C_4], H_4) → I_4
  125. Rotate(I_4 + (Segment[E_4, F_4], 0), Angle[F_4 - E_4] + Angle[I_4 - H_4] - Angle[E_4 - D_4], I_4) → J_4
  126. Polygon(G_4, H_4, I_4, J_4) → a29, g_5, h_5, i_5, j_4
  127. Point(Circle[K_4, Segment[G_4, H_4]]) → L_4
  128. Rotate(L_4 + (Segment[H_4, I_4], 0), Angle[I_4 - H_4] + Angle[L_4 - K_4] - Angle[H_4 - G_4], L_4) → M_4
  129. Rotate(M_4 + (Segment[I_4, J_4], 0), Angle[J_4 - I_4] + Angle[M_4 - L_4] - Angle[I_4 - H_4], M_4) → N_4
  130. Polygon(K_4, L_4, M_4, N_4) → a30, k_4, l_4, m_4, n_4
  131. Polygon(A_9, B_9, 4) → a1_2, f_{10}, g_{10}, h_{10}, i_{10}, C_9, D_9
  132. Point(Circle[W_6, Segment[A_9, B_9]]) → Z_6
  133. Rotate(Z_6 + (Segment[B_9, C_9], 0), Angle[C_9 - B_9] + Angle[Z_6 - W_6] - Angle[B_9 - A_9], Z_6) → A_8
  134. Rotate(A_8 + (Segment[C_9, D_9], 0), Angle[D_9 - C_9] + Angle[A_8 - Z_6] - Angle[C_9 - B_9], A_8) → B_8
  135. Polygon(W_6, Z_6, A_8, B_8) → a31, w_6, z_7, a_7, b_7
  136. Point(Circle[C_8, Segment[W_6, Z_6]]) → D_8
  137. Rotate(D_8 + (Segment[Z_6, A_8], 0), Angle[A_8 - Z_6] + Angle[D_8 - C_8] - Angle[Z_6 - W_6], D_8) → E_7
  138. Rotate(E_7 + (Segment[A_8, B_8], 0), Angle[B_8 - A_8] + Angle[E_7 - D_8] - Angle[A_8 - Z_6], E_7) → F_7
  139. Polygon(C_8, D_8, E_7, F_7) → a32, c_7, d_7, e_7, f_9
  140. Point(Circle[G_7, Segment[C_8, D_8]]) → H_7
  141. Rotate(H_7 + (Segment[D_8, E_7], 0), Angle[E_7 - D_8] + Angle[H_7 - G_7] - Angle[D_8 - C_8], H_7) → I_7
  142. Rotate(I_7 + (Segment[E_7, F_7], 0), Angle[F_7 - E_7] + Angle[I_7 - H_7] - Angle[E_7 - D_8], I_7) → J_7
  143. Polygon(G_7, H_7, I_7, J_7) → a33, g_9, h_9, i_9, j_7
  144. Point(Circle[K_7, Segment[G_7, H_7]]) → L_7
  145. Rotate(L_7 + (Segment[H_7, I_7], 0), Angle[I_7 - H_7] + Angle[L_7 - K_7] - Angle[H_7 - G_7], L_7) → M_7
  146. Rotate(M_7 + (Segment[I_7, J_7], 0), Angle[J_7 - I_7] + Angle[M_7 - L_7] - Angle[I_7 - H_7], M_7) → N_7
  147. Polygon(K_7, L_7, M_7, N_7) → a34, k_7, l_7, m_7, n_7
  148. Point(Circle[O_4, Segment[K_7, L_7]]) → P_4
  149. Rotate(P_4 + (Segment[L_7, M_7], 0), Angle[M_7 - L_7] + Angle[P_4 - O_4] - Angle[L_7 - K_7], P_4) → Q_4
  150. Rotate(Q_4 + (Segment[M_7, N_7], 0), Angle[N_7 - M_7] + Angle[Q_4 - P_4] - Angle[M_7 - L_7], Q_4) → R_4
  151. Polygon(O_4, P_4, Q_4, R_4) → a35, o_4, p_4, q_4, r_4
  152. Point(Circle[S_4, Segment[O_4, P_4]]) → T_4
  153. Rotate(T_4 + (Segment[P_4, Q_4], 0), Angle[Q_4 - P_4] + Angle[T_4 - S_4] - Angle[P_4 - O_4], T_4) → U_4
  154. Rotate(U_4 + (Segment[Q_4, R_4], 0), Angle[R_4 - Q_4] + Angle[U_4 - T_4] - Angle[Q_4 - P_4], U_4) → V_4
  155. Polygon(S_4, T_4, U_4, V_4) → a36, s_4, t_4, u_3, v_3
  156. Point(Circle[W_5, Segment[S_4, T_4]]) → Z_5
  157. Rotate(Z_5 + (Segment[T_4, U_4], 0), Angle[U_4 - T_4] + Angle[Z_5 - W_5] - Angle[T_4 - S_4], Z_5) → A_7
  158. Rotate(A_7 + (Segment[U_4, V_4], 0), Angle[V_4 - U_4] + Angle[A_7 - Z_5] - Angle[U_4 - T_4], A_7) → B_7
  159. Polygon(W_5, Z_5, A_7, B_7) → a37, w_5, z_6, a_6, b_6
  160. Point(Circle[C_7, Segment[W_5, Z_5]]) → D_7
  161. Rotate(D_7 + (Segment[Z_5, A_7], 0), Angle[A_7 - Z_5] + Angle[D_7 - C_7] - Angle[Z_5 - W_5], D_7) → E_6
  162. Rotate(E_6 + (Segment[A_7, B_7], 0), Angle[B_7 - A_7] + Angle[E_6 - D_7] - Angle[A_7 - Z_5], E_6) → F_6
  163. Polygon(C_7, D_7, E_6, F_6) → a38, c_6, d_6, e_6, f_8
  164. Point(Circle[G_6, Segment[C_7, D_7]]) → H_6
  165. Rotate(H_6 + (Segment[D_7, E_6], 0), Angle[E_6 - D_7] + Angle[H_6 - G_6] - Angle[D_7 - C_7], H_6) → I_6
  166. Rotate(I_6 + (Segment[E_6, F_6], 0), Angle[F_6 - E_6] + Angle[I_6 - H_6] - Angle[E_6 - D_7], I_6) → J_6
  167. Polygon(G_6, H_6, I_6, J_6) → a39, g_8, h_8, i_8, j_6
  168. Point(Circle[K_6, Segment[G_6, H_6]]) → L_6
  169. Rotate(L_6 + (Segment[H_6, I_6], 0), Angle[I_6 - H_6] + Angle[L_6 - K_6] - Angle[H_6 - G_6], L_6) → M_6
  170. Rotate(M_6 + (Segment[I_6, J_6], 0), Angle[J_6 - I_6] + Angle[M_6 - L_6] - Angle[I_6 - H_6], M_6) → N_6
  171. Polygon(K_6, L_6, M_6, N_6) → a40, k_6, l_6, m_6, n_6
  172. Polygon(A_{12}, B_{12}, 4) → a1_3, f_{13}, g_{13}, h_{13}, i_{13}, C_{12}, D_{12}
  173. Point(Circle[W_8, Segment[A_{12}, B_{12}]]) → Z_8
  174. Rotate(Z_8 + (Segment[B_{12}, C_{12}], 0), Angle[C_{12} - B_{12}] + Angle[Z_8 - W_8] - Angle[B_{12} - A_{12}], Z_8) → A_{11}
  175. Rotate(A_{11} + (Segment[C_{12}, D_{12}], 0), Angle[D_{12} - C_{12}] + Angle[A_{11} - Z_8] - Angle[C_{12} - B_{12}], A_{11}) → B_{11}
  176. Polygon(W_8, Z_8, A_{11}, B_{11}) → a41, w_8, z_9, a_9, b_9
  177. Point(Circle[C_{11}, Segment[W_8, Z_8]]) → D_{11}
  178. Rotate(D_{11} + (Segment[Z_8, A_{11}], 0), Angle[A_{11} - Z_8] + Angle[D_{11} - C_{11}] - Angle[Z_8 - W_8], D_{11}) → E_9
  179. Rotate(E_9 + (Segment[A_{11}, B_{11}], 0), Angle[B_{11} - A_{11}] + Angle[E_9 - D_{11}] - Angle[A_{11} - Z_8], E_9) → F_9
  180. Polygon(C_{11}, D_{11}, E_9, F_9) → a42, c_9, d_9, e_9, f_{12}
  181. Point(Circle[G_9, Segment[C_{11}, D_{11}]]) → H_9
  182. Rotate(H_9 + (Segment[D_{11}, E_9], 0), Angle[E_9 - D_{11}] + Angle[H_9 - G_9] - Angle[D_{11} - C_{11}], H_9) → I_9
  183. Rotate(I_9 + (Segment[E_9, F_9], 0), Angle[F_9 - E_9] + Angle[I_9 - H_9] - Angle[E_9 - D_{11}], I_9) → J_9
  184. Polygon(G_9, H_9, I_9, J_9) → a43, g_{12}, h_{12}, i_{12}, j_9
  185. Point(Circle[K_9, Segment[G_9, H_9]]) → L_9
  186. Rotate(L_9 + (Segment[H_9, I_9], 0), Angle[I_9 - H_9] + Angle[L_9 - K_9] - Angle[H_9 - G_9], L_9) → M_9
  187. Rotate(M_9 + (Segment[I_9, J_9], 0), Angle[J_9 - I_9] + Angle[M_9 - L_9] - Angle[I_9 - H_9], M_9) → N_9
  188. Polygon(K_9, L_9, M_9, N_9) → a44, k_9, l_9, m_9, n_9
  189. Point(Circle[O_5, Segment[K_9, L_9]]) → P_5
  190. Rotate(P_5 + (Segment[L_9, M_9], 0), Angle[M_9 - L_9] + Angle[P_5 - O_5] - Angle[L_9 - K_9], P_5) → Q_5
  191. Rotate(Q_5 + (Segment[M_9, N_9], 0), Angle[N_9 - M_9] + Angle[Q_5 - P_5] - Angle[M_9 - L_9], Q_5) → R_5
  192. Polygon(O_5, P_5, Q_5, R_5) → a45, o_5, p_5, q_5, r_5
  193. Point(Circle[S_5, Segment[O_5, P_5]]) → T_5
  194. Rotate(T_5 + (Segment[P_5, Q_5], 0), Angle[Q_5 - P_5] + Angle[T_5 - S_5] - Angle[P_5 - O_5], T_5) → U_5
  195. Rotate(U_5 + (Segment[Q_5, R_5], 0), Angle[R_5 - Q_5] + Angle[U_5 - T_5] - Angle[Q_5 - P_5], U_5) → V_5
  196. Polygon(S_5, T_5, U_5, V_5) → a46, s_5, t_5, u_4, v_4
  197. Point(Circle[W_7, Segment[S_5, T_5]]) → Z_7
  198. Rotate(Z_7 + (Segment[T_5, U_5], 0), Angle[U_5 - T_5] + Angle[Z_7 - W_7] - Angle[T_5 - S_5], Z_7) → A_{10}
  199. Rotate(A_{10} + (Segment[U_5, V_5], 0), Angle[V_5 - U_5] + Angle[A_{10} - Z_7] - Angle[U_5 - T_5], A_{10}) → B_{10}
  200. Polygon(W_7, Z_7, A_{10}, B_{10}) → a47, w_7, z_8, a_8, b_8
  201. Point(Circle[C_{10}, Segment[W_7, Z_7]]) → D_{10}
  202. Rotate(D_{10} + (Segment[Z_7, A_{10}], 0), Angle[A_{10} - Z_7] + Angle[D_{10} - C_{10}] - Angle[Z_7 - W_7], D_{10}) → E_8
  203. Rotate(E_8 + (Segment[A_{10}, B_{10}], 0), Angle[B_{10} - A_{10}] + Angle[E_8 - D_{10}] - Angle[A_{10} - Z_7], E_8) → F_8
  204. Polygon(C_{10}, D_{10}, E_8, F_8) → a48, c_8, d_8, e_8, f_{11}
  205. Point(Circle[G_8, Segment[C_{10}, D_{10}]]) → H_8
  206. Rotate(H_8 + (Segment[D_{10}, E_8], 0), Angle[E_8 - D_{10}] + Angle[H_8 - G_8] - Angle[D_{10} - C_{10}], H_8) → I_8
  207. Rotate(I_8 + (Segment[E_8, F_8], 0), Angle[F_8 - E_8] + Angle[I_8 - H_8] - Angle[E_8 - D_{10}], I_8) → J_8
  208. Polygon(G_8, H_8, I_8, J_8) → a49, g_{11}, h_{11}, i_{11}, j_8
  209. Point(Circle[K_8, Segment[G_8, H_8]]) → L_8
  210. Rotate(L_8 + (Segment[H_8, I_8], 0), Angle[I_8 - H_8] + Angle[L_8 - K_8] - Angle[H_8 - G_8], L_8) → M_8
  211. Rotate(M_8 + (Segment[I_8, J_8], 0), Angle[J_8 - I_8] + Angle[M_8 - L_8] - Angle[I_8 - H_8], M_8) → N_8
  212. Polygon(K_8, L_8, M_8, N_8) → a50, k_8, l_8, m_8, n_8
  213. Polygon(A_{15}, B_{15}, 4) → a1_4, f_{16}, g_{16}, h_{16}, i_{16}, C_{15}, D_{15}
  214. Point(Circle[W_{10}, Segment[A_{15}, B_{15}]]) → Z_{10}
  215. Rotate(Z_{10} + (Segment[B_{15}, C_{15}], 0), Angle[C_{15} - B_{15}] + Angle[Z_{10} - W_{10}] - Angle[B_{15} - A_{15}], Z_{10}) → A_{14}
  216. Rotate(A_{14} + (Segment[C_{15}, D_{15}], 0), Angle[D_{15} - C_{15}] + Angle[A_{14} - Z_{10}] - Angle[C_{15} - B_{15}], A_{14}) → B_{14}
  217. Polygon(W_{10}, Z_{10}, A_{14}, B_{14}) → a51, w_{10}, z_{11}, a_{11}, b_{11}
  218. Point(Circle[C_{14}, Segment[W_{10}, Z_{10}]]) → D_{14}
  219. Rotate(D_{14} + (Segment[Z_{10}, A_{14}], 0), Angle[A_{14} - Z_{10}] + Angle[D_{14} - C_{14}] - Angle[Z_{10} - W_{10}], D_{14}) → E_{11}
  220. Rotate(E_{11} + (Segment[A_{14}, B_{14}], 0), Angle[B_{14} - A_{14}] + Angle[E_{11} - D_{14}] - Angle[A_{14} - Z_{10}], E_{11}) → F_{11}
  221. Polygon(C_{14}, D_{14}, E_{11}, F_{11}) → a52, c_{11}, d_{11}, e_{11}, f_{15}
  222. Point(Circle[G_{11}, Segment[C_{14}, D_{14}]]) → H_{11}
  223. Rotate(H_{11} + (Segment[D_{14}, E_{11}], 0), Angle[E_{11} - D_{14}] + Angle[H_{11} - G_{11}] - Angle[D_{14} - C_{14}], H_{11}) → I_{11}
  224. Rotate(I_{11} + (Segment[E_{11}, F_{11}], 0), Angle[F_{11} - E_{11}] + Angle[I_{11} - H_{11}] - Angle[E_{11} - D_{14}], I_{11}) → J_{11}
  225. Polygon(G_{11}, H_{11}, I_{11}, J_{11}) → a53, g_{15}, h_{15}, i_{15}, j_{11}
  226. Point(Circle[K_{11}, Segment[G_{11}, H_{11}]]) → L_{11}
  227. Rotate(L_{11} + (Segment[H_{11}, I_{11}], 0), Angle[I_{11} - H_{11}] + Angle[L_{11} - K_{11}] - Angle[H_{11} - G_{11}], L_{11}) → M_{11}
  228. Rotate(M_{11} + (Segment[I_{11}, J_{11}], 0), Angle[J_{11} - I_{11}] + Angle[M_{11} - L_{11}] - Angle[I_{11} - H_{11}], M_{11}) → N_{11}
  229. Polygon(K_{11}, L_{11}, M_{11}, N_{11}) → a54, k_{11}, l_{11}, m_{11}, n_{11}
  230. Point(Circle[O_6, Segment[K_{11}, L_{11}]]) → P_6
  231. Rotate(P_6 + (Segment[L_{11}, M_{11}], 0), Angle[M_{11} - L_{11}] + Angle[P_6 - O_6] - Angle[L_{11} - K_{11}], P_6) → Q_6
  232. Rotate(Q_6 + (Segment[M_{11}, N_{11}], 0), Angle[N_{11} - M_{11}] + Angle[Q_6 - P_6] - Angle[M_{11} - L_{11}], Q_6) → R_6
  233. Polygon(O_6, P_6, Q_6, R_6) → a55, o_6, p_6, q_6, r_6
  234. Point(Circle[S_6, Segment[O_6, P_6]]) → T_6
  235. Rotate(T_6 + (Segment[P_6, Q_6], 0), Angle[Q_6 - P_6] + Angle[T_6 - S_6] - Angle[P_6 - O_6], T_6) → U_6
  236. Rotate(U_6 + (Segment[Q_6, R_6], 0), Angle[R_6 - Q_6] + Angle[U_6 - T_6] - Angle[Q_6 - P_6], U_6) → V_6
  237. Polygon(S_6, T_6, U_6, V_6) → a56, s_6, t_6, u_5, v_5
  238. Point(Circle[W_9, Segment[S_6, T_6]]) → Z_9
  239. Rotate(Z_9 + (Segment[T_6, U_6], 0), Angle[U_6 - T_6] + Angle[Z_9 - W_9] - Angle[T_6 - S_6], Z_9) → A_{13}
  240. Rotate(A_{13} + (Segment[U_6, V_6], 0), Angle[V_6 - U_6] + Angle[A_{13} - Z_9] - Angle[U_6 - T_6], A_{13}) → B_{13}
  241. Polygon(W_9, Z_9, A_{13}, B_{13}) → a57, w_9, z_{10}, a_{10}, b_{10}
  242. Point(Circle[C_{13}, Segment[W_9, Z_9]]) → D_{13}
  243. Rotate(D_{13} + (Segment[Z_9, A_{13}], 0), Angle[A_{13} - Z_9] + Angle[D_{13} - C_{13}] - Angle[Z_9 - W_9], D_{13}) → E_{10}
  244. Rotate(E_{10} + (Segment[A_{13}, B_{13}], 0), Angle[B_{13} - A_{13}] + Angle[E_{10} - D_{13}] - Angle[A_{13} - Z_9], E_{10}) → F_{10}
  245. Polygon(C_{13}, D_{13}, E_{10}, F_{10}) → a58, c_{10}, d_{10}, e_{10}, f_{14}
  246. Point(Circle[G_{10}, Segment[C_{13}, D_{13}]]) → H_{10}
  247. Rotate(H_{10} + (Segment[D_{13}, E_{10}], 0), Angle[E_{10} - D_{13}] + Angle[H_{10} - G_{10}] - Angle[D_{13} - C_{13}], H_{10}) → I_{10}
  248. Rotate(I_{10} + (Segment[E_{10}, F_{10}], 0), Angle[F_{10} - E_{10}] + Angle[I_{10} - H_{10}] - Angle[E_{10} - D_{13}], I_{10}) → J_{10}
  249. Polygon(G_{10}, H_{10}, I_{10}, J_{10}) → a59, g_{14}, h_{14}, i_{14}, j_{10}
  250. Point(Circle[K_{10}, Segment[G_{10}, H_{10}]]) → L_{10}
  251. Rotate(L_{10} + (Segment[H_{10}, I_{10}], 0), Angle[I_{10} - H_{10}] + Angle[L_{10} - K_{10}] - Angle[H_{10} - G_{10}], L_{10}) → M_{10}
  252. Rotate(M_{10} + (Segment[I_{10}, J_{10}], 0), Angle[J_{10} - I_{10}] + Angle[M_{10} - L_{10}] - Angle[I_{10} - H_{10}], M_{10}) → N_{10}
  253. Polygon(K_{10}, L_{10}, M_{10}, N_{10}) → a60, k_{10}, l_{10}, m_{10}, n_{10}
  254. Polygon(A_{18}, B_{18}, 4) → a1_5, f_{19}, g_{19}, h_{19}, i_{19}, C_{18}, D_{18}
  255. Point(Circle[W_{12}, Segment[A_{18}, B_{18}]]) → Z_{12}
  256. Rotate(Z_{12} + (Segment[B_{18}, C_{18}], 0), Angle[C_{18} - B_{18}] + Angle[Z_{12} - W_{12}] - Angle[B_{18} - A_{18}], Z_{12}) → A_{17}
  257. Rotate(A_{17} + (Segment[C_{18}, D_{18}], 0), Angle[D_{18} - C_{18}] + Angle[A_{17} - Z_{12}] - Angle[C_{18} - B_{18}], A_{17}) → B_{17}
  258. Polygon(W_{12}, Z_{12}, A_{17}, B_{17}) → a61, w_{12}, z_{13}, a_{13}, b_{13}
  259. Point(Circle[C_{17}, Segment[W_{12}, Z_{12}]]) → D_{17}
  260. Rotate(D_{17} + (Segment[Z_{12}, A_{17}], 0), Angle[A_{17} - Z_{12}] + Angle[D_{17} - C_{17}] - Angle[Z_{12} - W_{12}], D_{17}) → E_{13}
  261. Rotate(E_{13} + (Segment[A_{17}, B_{17}], 0), Angle[B_{17} - A_{17}] + Angle[E_{13} - D_{17}] - Angle[A_{17} - Z_{12}], E_{13}) → F_{13}
  262. Polygon(C_{17}, D_{17}, E_{13}, F_{13}) → a62, c_{13}, d_{13}, e_{13}, f_{18}
  263. Point(Circle[G_{13}, Segment[C_{17}, D_{17}]]) → H_{13}
  264. Rotate(H_{13} + (Segment[D_{17}, E_{13}], 0), Angle[E_{13} - D_{17}] + Angle[H_{13} - G_{13}] - Angle[D_{17} - C_{17}], H_{13}) → I_{13}
  265. Rotate(I_{13} + (Segment[E_{13}, F_{13}], 0), Angle[F_{13} - E_{13}] + Angle[I_{13} - H_{13}] - Angle[E_{13} - D_{17}], I_{13}) → J_{13}
  266. Polygon(G_{13}, H_{13}, I_{13}, J_{13}) → a63, g_{18}, h_{18}, i_{18}, j_{13}
  267. Point(Circle[K_{13}, Segment[G_{13}, H_{13}]]) → L_{13}
  268. Rotate(L_{13} + (Segment[H_{13}, I_{13}], 0), Angle[I_{13} - H_{13}] + Angle[L_{13} - K_{13}] - Angle[H_{13} - G_{13}], L_{13}) → M_{13}
  269. Rotate(M_{13} + (Segment[I_{13}, J_{13}], 0), Angle[J_{13} - I_{13}] + Angle[M_{13} - L_{13}] - Angle[I_{13} - H_{13}], M_{13}) → N_{13}
  270. Polygon(K_{13}, L_{13}, M_{13}, N_{13}) → a64, k_{13}, l_{13}, m_{13}, n_{13}
  271. Point(Circle[O_7, Segment[K_{13}, L_{13}]]) → P_7
  272. Rotate(P_7 + (Segment[L_{13}, M_{13}], 0), Angle[M_{13} - L_{13}] + Angle[P_7 - O_7] - Angle[L_{13} - K_{13}], P_7) → Q_7
  273. Rotate(Q_7 + (Segment[M_{13}, N_{13}], 0), Angle[N_{13} - M_{13}] + Angle[Q_7 - P_7] - Angle[M_{13} - L_{13}], Q_7) → R_7
  274. Polygon(O_7, P_7, Q_7, R_7) → a65, o_7, p_7, q_7, r_7
  275. Point(Circle[S_7, Segment[O_7, P_7]]) → T_7
  276. Rotate(T_7 + (Segment[P_7, Q_7], 0), Angle[Q_7 - P_7] + Angle[T_7 - S_7] - Angle[P_7 - O_7], T_7) → U_7
  277. Rotate(U_7 + (Segment[Q_7, R_7], 0), Angle[R_7 - Q_7] + Angle[U_7 - T_7] - Angle[Q_7 - P_7], U_7) → V_7
  278. Polygon(S_7, T_7, U_7, V_7) → a66, s_7, t_7, u_6, v_6
  279. Point(Circle[W_{11}, Segment[S_7, T_7]]) → Z_{11}
  280. Rotate(Z_{11} + (Segment[T_7, U_7], 0), Angle[U_7 - T_7] + Angle[Z_{11} - W_{11}] - Angle[T_7 - S_7], Z_{11}) → A_{16}
  281. Rotate(A_{16} + (Segment[U_7, V_7], 0), Angle[V_7 - U_7] + Angle[A_{16} - Z_{11}] - Angle[U_7 - T_7], A_{16}) → B_{16}
  282. Polygon(W_{11}, Z_{11}, A_{16}, B_{16}) → a67, w_{11}, z_{12}, a_{12}, b_{12}
  283. Point(Circle[C_{16}, Segment[W_{11}, Z_{11}]]) → D_{16}
  284. Rotate(D_{16} + (Segment[Z_{11}, A_{16}], 0), Angle[A_{16} - Z_{11}] + Angle[D_{16} - C_{16}] - Angle[Z_{11} - W_{11}], D_{16}) → E_{12}
  285. Rotate(E_{12} + (Segment[A_{16}, B_{16}], 0), Angle[B_{16} - A_{16}] + Angle[E_{12} - D_{16}] - Angle[A_{16} - Z_{11}], E_{12}) → F_{12}
  286. Polygon(C_{16}, D_{16}, E_{12}, F_{12}) → a68, c_{12}, d_{12}, e_{12}, f_{17}
  287. Point(Circle[G_{12}, Segment[C_{16}, D_{16}]]) → H_{12}
  288. Rotate(H_{12} + (Segment[D_{16}, E_{12}], 0), Angle[E_{12} - D_{16}] + Angle[H_{12} - G_{12}] - Angle[D_{16} - C_{16}], H_{12}) → I_{12}
  289. Rotate(I_{12} + (Segment[E_{12}, F_{12}], 0), Angle[F_{12} - E_{12}] + Angle[I_{12} - H_{12}] - Angle[E_{12} - D_{16}], I_{12}) → J_{12}
  290. Polygon(G_{12}, H_{12}, I_{12}, J_{12}) → a69, g_{17}, h_{17}, i_{17}, j_{12}
  291. Point(Circle[K_{12}, Segment[G_{12}, H_{12}]]) → L_{12}
  292. Rotate(L_{12} + (Segment[H_{12}, I_{12}], 0), Angle[I_{12} - H_{12}] + Angle[L_{12} - K_{12}] - Angle[H_{12} - G_{12}], L_{12}) → M_{12}
  293. Rotate(M_{12} + (Segment[I_{12}, J_{12}], 0), Angle[J_{12} - I_{12}] + Angle[M_{12} - L_{12}] - Angle[I_{12} - H_{12}], M_{12}) → N_{12}
  294. Polygon(K_{12}, L_{12}, M_{12}, N_{12}) → a70, k_{12}, l_{12}, m_{12}, n_{12}
  295. Polygon(A_{21}, B_{21}, 4) → a1_6, f_{22}, g_{22}, h_{22}, i_{22}, C_{21}, D_{21}
  296. Point(Circle[W_{14}, Segment[A_{21}, B_{21}]]) → Z_{14}
  297. Rotate(Z_{14} + (Segment[B_{21}, C_{21}], 0), Angle[C_{21} - B_{21}] + Angle[Z_{14} - W_{14}] - Angle[B_{21} - A_{21}], Z_{14}) → A_{20}
  298. Rotate(A_{20} + (Segment[C_{21}, D_{21}], 0), Angle[D_{21} - C_{21}] + Angle[A_{20} - Z_{14}] - Angle[C_{21} - B_{21}], A_{20}) → B_{20}
  299. Polygon(W_{14}, Z_{14}, A_{20}, B_{20}) → a71, w_{14}, z_{15}, a_{15}, b_{15}
  300. Point(Circle[C_{20}, Segment[W_{14}, Z_{14}]]) → D_{20}
  301. Rotate(D_{20} + (Segment[Z_{14}, A_{20}], 0), Angle[A_{20} - Z_{14}] + Angle[D_{20} - C_{20}] - Angle[Z_{14} - W_{14}], D_{20}) → E_{15}
  302. Rotate(E_{15} + (Segment[A_{20}, B_{20}], 0), Angle[B_{20} - A_{20}] + Angle[E_{15} - D_{20}] - Angle[A_{20} - Z_{14}], E_{15}) → F_{15}
  303. Polygon(C_{20}, D_{20}, E_{15}, F_{15}) → a72, c_{15}, d_{15}, e_{15}, f_{21}
  304. Point(Circle[G_{15}, Segment[C_{20}, D_{20}]]) → H_{15}
  305. Rotate(H_{15} + (Segment[D_{20}, E_{15}], 0), Angle[E_{15} - D_{20}] + Angle[H_{15} - G_{15}] - Angle[D_{20} - C_{20}], H_{15}) → I_{15}
  306. Rotate(I_{15} + (Segment[E_{15}, F_{15}], 0), Angle[F_{15} - E_{15}] + Angle[I_{15} - H_{15}] - Angle[E_{15} - D_{20}], I_{15}) → J_{15}
  307. Polygon(G_{15}, H_{15}, I_{15}, J_{15}) → a73, g_{21}, h_{21}, i_{21}, j_{15}
  308. Point(Circle[K_{15}, Segment[G_{15}, H_{15}]]) → L_{15}
  309. Rotate(L_{15} + (Segment[H_{15}, I_{15}], 0), Angle[I_{15} - H_{15}] + Angle[L_{15} - K_{15}] - Angle[H_{15} - G_{15}], L_{15}) → M_{15}
  310. Rotate(M_{15} + (Segment[I_{15}, J_{15}], 0), Angle[J_{15} - I_{15}] + Angle[M_{15} - L_{15}] - Angle[I_{15} - H_{15}], M_{15}) → N_{15}
  311. Polygon(K_{15}, L_{15}, M_{15}, N_{15}) → a74, k_{15}, l_{15}, m_{15}, n_{15}
  312. Point(Circle[O_8, Segment[K_{15}, L_{15}]]) → P_8
  313. Rotate(P_8 + (Segment[L_{15}, M_{15}], 0), Angle[M_{15} - L_{15}] + Angle[P_8 - O_8] - Angle[L_{15} - K_{15}], P_8) → Q_8
  314. Rotate(Q_8 + (Segment[M_{15}, N_{15}], 0), Angle[N_{15} - M_{15}] + Angle[Q_8 - P_8] - Angle[M_{15} - L_{15}], Q_8) → R_8
  315. Polygon(O_8, P_8, Q_8, R_8) → a75, o_8, p_8, q_8, r_8
  316. Point(Circle[S_8, Segment[O_8, P_8]]) → T_8
  317. Rotate(T_8 + (Segment[P_8, Q_8], 0), Angle[Q_8 - P_8] + Angle[T_8 - S_8] - Angle[P_8 - O_8], T_8) → U_8
  318. Rotate(U_8 + (Segment[Q_8, R_8], 0), Angle[R_8 - Q_8] + Angle[U_8 - T_8] - Angle[Q_8 - P_8], U_8) → V_8
  319. Polygon(S_8, T_8, U_8, V_8) → a76, s_8, t_8, u_7, v_7
  320. Point(Circle[W_{13}, Segment[S_8, T_8]]) → Z_{13}
  321. Rotate(Z_{13} + (Segment[T_8, U_8], 0), Angle[U_8 - T_8] + Angle[Z_{13} - W_{13}] - Angle[T_8 - S_8], Z_{13}) → A_{19}
  322. Rotate(A_{19} + (Segment[U_8, V_8], 0), Angle[V_8 - U_8] + Angle[A_{19} - Z_{13}] - Angle[U_8 - T_8], A_{19}) → B_{19}
  323. Polygon(W_{13}, Z_{13}, A_{19}, B_{19}) → a77, w_{13}, z_{14}, a_{14}, b_{14}
  324. Point(Circle[C_{19}, Segment[W_{13}, Z_{13}]]) → D_{19}
  325. Rotate(D_{19} + (Segment[Z_{13}, A_{19}], 0), Angle[A_{19} - Z_{13}] + Angle[D_{19} - C_{19}] - Angle[Z_{13} - W_{13}], D_{19}) → E_{14}
  326. Rotate(E_{14} + (Segment[A_{19}, B_{19}], 0), Angle[B_{19} - A_{19}] + Angle[E_{14} - D_{19}] - Angle[A_{19} - Z_{13}], E_{14}) → F_{14}
  327. Polygon(C_{19}, D_{19}, E_{14}, F_{14}) → a78, c_{14}, d_{14}, e_{14}, f_{20}
  328. Point(Circle[G_{14}, Segment[C_{19}, D_{19}]]) → H_{14}
  329. Rotate(H_{14} + (Segment[D_{19}, E_{14}], 0), Angle[E_{14} - D_{19}] + Angle[H_{14} - G_{14}] - Angle[D_{19} - C_{19}], H_{14}) → I_{14}
  330. Rotate(I_{14} + (Segment[E_{14}, F_{14}], 0), Angle[F_{14} - E_{14}] + Angle[I_{14} - H_{14}] - Angle[E_{14} - D_{19}], I_{14}) → J_{14}
  331. Polygon(G_{14}, H_{14}, I_{14}, J_{14}) → a79, g_{20}, h_{20}, i_{20}, j_{14}
  332. Point(Circle[K_{14}, Segment[G_{14}, H_{14}]]) → L_{14}
  333. Rotate(L_{14} + (Segment[H_{14}, I_{14}], 0), Angle[I_{14} - H_{14}] + Angle[L_{14} - K_{14}] - Angle[H_{14} - G_{14}], L_{14}) → M_{14}
  334. Rotate(M_{14} + (Segment[I_{14}, J_{14}], 0), Angle[J_{14} - I_{14}] + Angle[M_{14} - L_{14}] - Angle[I_{14} - H_{14}], M_{14}) → N_{14}
  335. Polygon(K_{14}, L_{14}, M_{14}, N_{14}) → a80, k_{14}, l_{14}, m_{14}, n_{14}
  336. Polygon(A_{24}, B_{24}, 4) → a1_7, f_{25}, g_{25}, h_{25}, i_{25}, C_{24}, D_{24}
  337. Point(Circle[W_{16}, Segment[A_{24}, B_{24}]]) → Z_{16}
  338. Rotate(Z_{16} + (Segment[B_{24}, C_{24}], 0), Angle[C_{24} - B_{24}] + Angle[Z_{16} - W_{16}] - Angle[B_{24} - A_{24}], Z_{16}) → A_{23}
  339. Rotate(A_{23} + (Segment[C_{24}, D_{24}], 0), Angle[D_{24} - C_{24}] + Angle[A_{23} - Z_{16}] - Angle[C_{24} - B_{24}], A_{23}) → B_{23}
  340. Polygon(W_{16}, Z_{16}, A_{23}, B_{23}) → a81, w_{16}, z_{17}, a_{17}, b_{17}
  341. Point(Circle[C_{23}, Segment[W_{16}, Z_{16}]]) → D_{23}
  342. Rotate(D_{23} + (Segment[Z_{16}, A_{23}], 0), Angle[A_{23} - Z_{16}] + Angle[D_{23} - C_{23}] - Angle[Z_{16} - W_{16}], D_{23}) → E_{17}
  343. Rotate(E_{17} + (Segment[A_{23}, B_{23}], 0), Angle[B_{23} - A_{23}] + Angle[E_{17} - D_{23}] - Angle[A_{23} - Z_{16}], E_{17}) → F_{17}
  344. Polygon(C_{23}, D_{23}, E_{17}, F_{17}) → a82, c_{17}, d_{17}, e_{17}, f_{24}
  345. Point(Circle[G_{17}, Segment[C_{23}, D_{23}]]) → H_{17}
  346. Rotate(H_{17} + (Segment[D_{23}, E_{17}], 0), Angle[E_{17} - D_{23}] + Angle[H_{17} - G_{17}] - Angle[D_{23} - C_{23}], H_{17}) → I_{17}
  347. Rotate(I_{17} + (Segment[E_{17}, F_{17}], 0), Angle[F_{17} - E_{17}] + Angle[I_{17} - H_{17}] - Angle[E_{17} - D_{23}], I_{17}) → J_{17}
  348. Polygon(G_{17}, H_{17}, I_{17}, J_{17}) → a83, g_{24}, h_{24}, i_{24}, j_{17}
  349. Point(Circle[K_{17}, Segment[G_{17}, H_{17}]]) → L_{17}
  350. Rotate(L_{17} + (Segment[H_{17}, I_{17}], 0), Angle[I_{17} - H_{17}] + Angle[L_{17} - K_{17}] - Angle[H_{17} - G_{17}], L_{17}) → M_{17}
  351. Rotate(M_{17} + (Segment[I_{17}, J_{17}], 0), Angle[J_{17} - I_{17}] + Angle[M_{17} - L_{17}] - Angle[I_{17} - H_{17}], M_{17}) → N_{17}
  352. Polygon(K_{17}, L_{17}, M_{17}, N_{17}) → a84, k_{17}, l_{17}, m_{17}, n_{17}
  353. Point(Circle[O_9, Segment[K_{17}, L_{17}]]) → P_9
  354. Rotate(P_9 + (Segment[L_{17}, M_{17}], 0), Angle[M_{17} - L_{17}] + Angle[P_9 - O_9] - Angle[L_{17} - K_{17}], P_9) → Q_9
  355. Rotate(Q_9 + (Segment[M_{17}, N_{17}], 0), Angle[N_{17} - M_{17}] + Angle[Q_9 - P_9] - Angle[M_{17} - L_{17}], Q_9) → R_9
  356. Polygon(O_9, P_9, Q_9, R_9) → a85, o_9, p_9, q_9, r_9
  357. Point(Circle[S_9, Segment[O_9, P_9]]) → T_9
  358. Rotate(T_9 + (Segment[P_9, Q_9], 0), Angle[Q_9 - P_9] + Angle[T_9 - S_9] - Angle[P_9 - O_9], T_9) → U_9
  359. Rotate(U_9 + (Segment[Q_9, R_9], 0), Angle[R_9 - Q_9] + Angle[U_9 - T_9] - Angle[Q_9 - P_9], U_9) → V_9
  360. Polygon(S_9, T_9, U_9, V_9) → a86, s_9, t_9, u_8, v_8
  361. Point(Circle[W_{15}, Segment[S_9, T_9]]) → Z_{15}
  362. Rotate(Z_{15} + (Segment[T_9, U_9], 0), Angle[U_9 - T_9] + Angle[Z_{15} - W_{15}] - Angle[T_9 - S_9], Z_{15}) → A_{22}
  363. Rotate(A_{22} + (Segment[U_9, V_9], 0), Angle[V_9 - U_9] + Angle[A_{22} - Z_{15}] - Angle[U_9 - T_9], A_{22}) → B_{22}
  364. Polygon(W_{15}, Z_{15}, A_{22}, B_{22}) → a87, w_{15}, z_{16}, a_{16}, b_{16}
  365. Point(Circle[C_{22}, Segment[W_{15}, Z_{15}]]) → D_{22}
  366. Rotate(D_{22} + (Segment[Z_{15}, A_{22}], 0), Angle[A_{22} - Z_{15}] + Angle[D_{22} - C_{22}] - Angle[Z_{15} - W_{15}], D_{22}) → E_{16}
  367. Rotate(E_{16} + (Segment[A_{22}, B_{22}], 0), Angle[B_{22} - A_{22}] + Angle[E_{16} - D_{22}] - Angle[A_{22} - Z_{15}], E_{16}) → F_{16}
  368. Polygon(C_{22}, D_{22}, E_{16}, F_{16}) → a88, c_{16}, d_{16}, e_{16}, f_{23}
  369. Point(Circle[G_{16}, Segment[C_{22}, D_{22}]]) → H_{16}
  370. Rotate(H_{16} + (Segment[D_{22}, E_{16}], 0), Angle[E_{16} - D_{22}] + Angle[H_{16} - G_{16}] - Angle[D_{22} - C_{22}], H_{16}) → I_{16}
  371. Rotate(I_{16} + (Segment[E_{16}, F_{16}], 0), Angle[F_{16} - E_{16}] + Angle[I_{16} - H_{16}] - Angle[E_{16} - D_{22}], I_{16}) → J_{16}
  372. Polygon(G_{16}, H_{16}, I_{16}, J_{16}) → a89, g_{23}, h_{23}, i_{23}, j_{16}
  373. Point(Circle[K_{16}, Segment[G_{16}, H_{16}]]) → L_{16}
  374. Rotate(L_{16} + (Segment[H_{16}, I_{16}], 0), Angle[I_{16} - H_{16}] + Angle[L_{16} - K_{16}] - Angle[H_{16} - G_{16}], L_{16}) → M_{16}
  375. Rotate(M_{16} + (Segment[I_{16}, J_{16}], 0), Angle[J_{16} - I_{16}] + Angle[M_{16} - L_{16}] - Angle[I_{16} - H_{16}], M_{16}) → N_{16}
  376. Polygon(K_{16}, L_{16}, M_{16}, N_{16}) → a90, k_{16}, l_{16}, m_{16}, n_{16}
  377. Polygon(A_{27}, B_{27}, 4) → a1_8, f_{28}, g_{28}, h_{28}, i_{28}, C_{27}, D_{27}
  378. Point(Circle[W_{18}, Segment[A_{27}, B_{27}]]) → Z_{18}
  379. Rotate(Z_{18} + (Segment[B_{27}, C_{27}], 0), Angle[C_{27} - B_{27}] + Angle[Z_{18} - W_{18}] - Angle[B_{27} - A_{27}], Z_{18}) → A_{26}
  380. Rotate(A_{26} + (Segment[C_{27}, D_{27}], 0), Angle[D_{27} - C_{27}] + Angle[A_{26} - Z_{18}] - Angle[C_{27} - B_{27}], A_{26}) → B_{26}
  381. Polygon(W_{18}, Z_{18}, A_{26}, B_{26}) → a91, w_{18}, z_{19}, a_{19}, b_{19}
  382. Point(Circle[C_{26}, Segment[W_{18}, Z_{18}]]) → D_{26}
  383. Rotate(D_{26} + (Segment[Z_{18}, A_{26}], 0), Angle[A_{26} - Z_{18}] + Angle[D_{26} - C_{26}] - Angle[Z_{18} - W_{18}], D_{26}) → E_{19}
  384. Rotate(E_{19} + (Segment[A_{26}, B_{26}], 0), Angle[B_{26} - A_{26}] + Angle[E_{19} - D_{26}] - Angle[A_{26} - Z_{18}], E_{19}) → F_{19}
  385. Polygon(C_{26}, D_{26}, E_{19}, F_{19}) → a92, c_{19}, d_{19}, e_{19}, f_{27}
  386. Point(Circle[G_{19}, Segment[C_{26}, D_{26}]]) → H_{19}
  387. Rotate(H_{19} + (Segment[D_{26}, E_{19}], 0), Angle[E_{19} - D_{26}] + Angle[H_{19} - G_{19}] - Angle[D_{26} - C_{26}], H_{19}) → I_{19}
  388. Rotate(I_{19} + (Segment[E_{19}, F_{19}], 0), Angle[F_{19} - E_{19}] + Angle[I_{19} - H_{19}] - Angle[E_{19} - D_{26}], I_{19}) → J_{19}
  389. Polygon(G_{19}, H_{19}, I_{19}, J_{19}) → a93, g_{27}, h_{27}, i_{27}, j_{19}
  390. Point(Circle[K_{19}, Segment[G_{19}, H_{19}]]) → L_{19}
  391. Rotate(L_{19} + (Segment[H_{19}, I_{19}], 0), Angle[I_{19} - H_{19}] + Angle[L_{19} - K_{19}] - Angle[H_{19} - G_{19}], L_{19}) → M_{19}
  392. Rotate(M_{19} + (Segment[I_{19}, J_{19}], 0), Angle[J_{19} - I_{19}] + Angle[M_{19} - L_{19}] - Angle[I_{19} - H_{19}], M_{19}) → N_{19}
  393. Polygon(K_{19}, L_{19}, M_{19}, N_{19}) → a94, k_{19}, l_{19}, m_{19}, n_{19}
  394. Point(Circle[O_{10}, Segment[K_{19}, L_{19}]]) → P_{10}
  395. Rotate(P_{10} + (Segment[L_{19}, M_{19}], 0), Angle[M_{19} - L_{19}] + Angle[P_{10} - O_{10}] - Angle[L_{19} - K_{19}], P_{10}) → Q_{10}
  396. Rotate(Q_{10} + (Segment[M_{19}, N_{19}], 0), Angle[N_{19} - M_{19}] + Angle[Q_{10} - P_{10}] - Angle[M_{19} - L_{19}], Q_{10}) → R_{10}
  397. Polygon(O_{10}, P_{10}, Q_{10}, R_{10}) → a95, o_{10}, p_{10}, q_{10}, r_{10}
  398. Point(Circle[S_{10}, Segment[O_{10}, P_{10}]]) → T_{10}
  399. Rotate(T_{10} + (Segment[P_{10}, Q_{10}], 0), Angle[Q_{10} - P_{10}] + Angle[T_{10} - S_{10}] - Angle[P_{10} - O_{10}], T_{10}) → U_{10}
  400. Rotate(U_{10} + (Segment[Q_{10}, R_{10}], 0), Angle[R_{10} - Q_{10}] + Angle[U_{10} - T_{10}] - Angle[Q_{10} - P_{10}], U_{10}) → V_{10}
  401. Polygon(S_{10}, T_{10}, U_{10}, V_{10}) → a96, s_{10}, t_{10}, u_9, v_9
  402. Point(Circle[W_{17}, Segment[S_{10}, T_{10}]]) → Z_{17}
  403. Rotate(Z_{17} + (Segment[T_{10}, U_{10}], 0), Angle[U_{10} - T_{10}] + Angle[Z_{17} - W_{17}] - Angle[T_{10} - S_{10}], Z_{17}) → A_{25}
  404. Rotate(A_{25} + (Segment[U_{10}, V_{10}], 0), Angle[V_{10} - U_{10}] + Angle[A_{25} - Z_{17}] - Angle[U_{10} - T_{10}], A_{25}) → B_{25}
  405. Polygon(W_{17}, Z_{17}, A_{25}, B_{25}) → a97, w_{17}, z_{18}, a_{18}, b_{18}
  406. Point(Circle[C_{25}, Segment[W_{17}, Z_{17}]]) → D_{25}
  407. Rotate(D_{25} + (Segment[Z_{17}, A_{25}], 0), Angle[A_{25} - Z_{17}] + Angle[D_{25} - C_{25}] - Angle[Z_{17} - W_{17}], D_{25}) → E_{18}
  408. Rotate(E_{18} + (Segment[A_{25}, B_{25}], 0), Angle[B_{25} - A_{25}] + Angle[E_{18} - D_{25}] - Angle[A_{25} - Z_{17}], E_{18}) → F_{18}
  409. Polygon(C_{25}, D_{25}, E_{18}, F_{18}) → a98, c_{18}, d_{18}, e_{18}, f_{26}
  410. Point(Circle[G_{18}, Segment[C_{25}, D_{25}]]) → H_{18}
  411. Rotate(H_{18} + (Segment[D_{25}, E_{18}], 0), Angle[E_{18} - D_{25}] + Angle[H_{18} - G_{18}] - Angle[D_{25} - C_{25}], H_{18}) → I_{18}
  412. Rotate(I_{18} + (Segment[E_{18}, F_{18}], 0), Angle[F_{18} - E_{18}] + Angle[I_{18} - H_{18}] - Angle[E_{18} - D_{25}], I_{18}) → J_{18}
  413. Polygon(G_{18}, H_{18}, I_{18}, J_{18}) → a99, g_{26}, h_{26}, i_{26}, j_{18}
  414. Point(Circle[K_{18}, Segment[G_{18}, H_{18}]]) → L_{18}
  415. Rotate(L_{18} + (Segment[H_{18}, I_{18}], 0), Angle[I_{18} - H_{18}] + Angle[L_{18} - K_{18}] - Angle[H_{18} - G_{18}], L_{18}) → M_{18}
  416. Rotate(M_{18} + (Segment[I_{18}, J_{18}], 0), Angle[J_{18} - I_{18}] + Angle[M_{18} - L_{18}] - Angle[I_{18} - H_{18}], M_{18}) → N_{18}
  417. Polygon(K_{18}, L_{18}, M_{18}, N_{18}) → a100, k_{18}, l_{18}, m_{18}, n_{18}
  418. Polygon(O_{11}, P_{11}, 4) → mnogokut1, b, p_{11}, q_{11}, r_{11}, Q_{11}, R_{11}
  419. Segment(O_{11}, Q_{11}) → s_{11}
  420. Segment(P_{11}, R_{11}) → t_{11}
  421. Intersect(s_{11}, t_{11}) → S_{11}
  422. Sequence(Sequence[Polygon[(i, j), (i + 1, j), 4], i, -3, 6, 1], j, -6, 3, 1) → lista1
  423. Polygon(T_{11}, U_{11}, 4) → mnogokut2, p_{12}, q_{12}, r_{12}, s_{12}, V_{11}, O_{12}
  424. Segment(T_{11}, V_{11}) → t_{12}
  425. Segment(U_{11}, O_{12}) → p_{13}
  426. Union(obojaniBrojevi, obojaniBrojevi) → obojBrBezPon
  427. RemoveUndefined(Sequence[If[Divisors[i] ≟ 2, i], i, 1, 100, 1]) → prostiBrojevi
  428. RemoveUndefined(Sequence[If[Divisors[i] > 2, i], i, 1, 100, 1]) → slozeniBrojevi
  429. RemoveUndefined(Sequence[If[Element[obojBrBezPon, i] ≤ 100, Element[obojBrBezPon, i]], i, 1, Length[obojBrBezPon], 1]) → obojBrBezPonSređ
  430. Circle(SredišteKvadrata[E, F], 0.4) → b2
  431. Circle(SredišteKvadrata[I, J], 0.4) → b3
  432. Circle(SredišteKvadrata[Q, R], 0.4) → b5
  433. Circle(SredišteKvadrata[A_1, B_1], 0.4) → b7
  434. Circle(SredišteKvadrata[W_1, Z_1], 0.4) → b11
  435. Circle(SredišteKvadrata[G_2, H_2], 0.4) → b13
  436. Circle(SredišteKvadrata[W_2, Z_2], 0.4) → b17
  437. Circle(SredišteKvadrata[G_3, H_3], 0.4) → b19
  438. Circle(SredišteKvadrata[G_5, H_5], 0.4) → b23
  439. Circle(SredišteKvadrata[G_4, H_4], 0.4) → b29
  440. Circle(SredišteKvadrata[W_6, Z_6], 0.4) → b31
  441. Circle(SredišteKvadrata[W_5, Z_5], 0.4) → b37
  442. Circle(SredišteKvadrata[W_8, Z_8], 0.4) → b41
  443. Circle(SredišteKvadrata[G_9, H_9], 0.4) → b43
  444. Circle(SredišteKvadrata[W_7, Z_7], 0.4) → b47
  445. Circle(SredišteKvadrata[G_{11}, H_{11}], 0.4) → b53
  446. Circle(SredišteKvadrata[G_{10}, H_{10}], 0.4) → b59
  447. Circle(SredišteKvadrata[W_{12}, Z_{12}], 0.4) → b61
  448. Circle(SredišteKvadrata[W_{11}, Z_{11}], 0.4) → b67
  449. Circle(SredišteKvadrata[W_{14}, Z_{14}], 0.4) → b71
  450. Circle(SredišteKvadrata[G_{15}, H_{15}], 0.4) → b73
  451. Circle(SredišteKvadrata[G_{14}, H_{14}], 0.4) → b79
  452. Circle(SredišteKvadrata[G_{17}, H_{17}], 0.4) → b83
  453. Circle(SredišteKvadrata[G_{16}, H_{16}], 0.4) → b89
  454. Circle(SredišteKvadrata[W_{17}, Z_{17}], 0.4) → b97

AI 绘图提示语参考

绘制埃拉托斯特尼筛法的动态演示。首先画一个四边形，然后围绕该四边形的边依次旋转生成新的四边形，重复此过程多次，形成一系列嵌套的四边形。最后，为每个顶点画一个小圆圈。
以上提示语为根据原始绘图命令整理而来，仅供参考。