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Pentago几何游戏

Pentago几何游戏
几何画板及绘图内容加载中，请稍等……
2017-09-08 07:45
多边形几何作图滑块动画
所属专题 GeoGebra day at MoMath
这个范例演示了Pentago游戏的几何原理。涉及的核心数学概念包括几何构造、滑块动画和轨迹。通过使用Polygon, Circle, Intersect, OrthogonalLine等GeoGebra命令，可以构建出Pentago游戏的棋盘和棋子移动的轨迹。适合初中及以上学生和教师使用，用于教学和学习几何游戏的策略。

GeoGebra 命令及参数

  1. Polygon(T_1, S_1, 3) → poly4, h_2, i_2, j_2, E_2
  2. Polygon(F_2, G_2, 3) → poly5, k_2, l_2, m_2, H_2
  3. Polygon(M_1, M_2, 4) → poly1, f, g, h, i, A, B
  4. Circle(M_1, 0.5) → c
  5. Intersect(c, f, 1) → C
  6. Circle(C, 1) → d
  7. Intersect(d, f) → D,
  8. Circle(D, 1) → k
  9. Intersect(k, f, 2) → I
  10. Intersect(c, i) → J,
  11. Circle(J, 1) → p
  12. Intersect(p, i, 1) → K
  13. Circle(K, 1) → q
  14. Intersect(q, i, 1) → L
  15. OrthogonalLine(C, f) → j
  16. OrthogonalLine(D, f) → l
  17. OrthogonalLine(I, f) → m
  18. OrthogonalLine(J, i) → r
  19. OrthogonalLine(K, i) → s
  20. OrthogonalLine(L, i) → t
  21. Intersect(j, t) → N
  22. Intersect(l, t) → O
  23. Intersect(m, t) → P
  24. Intersect(m, s) → Q_7
  25. Intersect(l, s) → R
  26. Intersect(j, s) → S
  27. Intersect(j, r) → T
  28. Intersect(l, r) → U
  29. Intersect(m, r) → V
  30. Circle(P, 0.3) → c_3
  31. Circle(Q_7, 0.3) → c_6
  32. Circle(V, 0.3) → c_9
  33. Circle(O, 0.3) → c_2
  34. Circle(R, 0.3) → c_5
  35. Circle(U, 0.3) → c_8
  36. Circle(N, 0.3) → c_1
  37. Circle(S, 0.3) → c_4
  38. Circle(T, 0.3) → c_7
  39. Circle(E, 0.6) → e
  40. Circle(E, 0.6) → d_{10}
  41. Polygon(N_1, N_2, N_3, N_4) → poly2, n_1, n_2, n_3, n_4
  42. Circle(N_1, 0.5) → e_{13}
  43. Intersect(e_{13}, n_1, 1) → F
  44. Circle(F, 1) → f_{12}
  45. Intersect(f_{12}, n_1) → G,
  46. Circle(G, 1) → g_1
  47. Intersect(g_1, n_1, 2) → H
  48. Intersect(e_{13}, n_4) → W,
  49. Circle(W, 1) → h_1
  50. Intersect(h_1, n_4, 1) → Z
  51. Circle(Z, 1) → k_1
  52. Intersect(k_1, n_4, 1) → A_1
  53. OrthogonalLine(A_1, n_4) → a
  54. OrthogonalLine(Z, n_4) → b
  55. OrthogonalLine(W, n_4) → i_1
  56. OrthogonalLine(F, n_1) → j_1
  57. OrthogonalLine(G, n_1) → l_1
  58. OrthogonalLine(H, n_1) → m_1
  59. Intersect(a, j_1) → B_1
  60. Intersect(a, l_1) → C_1
  61. Intersect(a, m_1) → D_1
  62. Intersect(b, l_1) → E_1
  63. Intersect(b, m_1) → G_1
  64. Intersect(i_1, m_1) → H_1
  65. Circle(B_1, 0.3) → d_1
  66. Circle(C_1, 0.3) → d_2
  67. Circle(D_1, 0.3) → d_3
  68. Circle(E_1, 0.3) → d_5
  69. Circle(G_1, 0.3) → d_6
  70. Circle(H_1, 0.3) → d_9
  71. Polygon(K_1, L_5, 3) → poly3, a_1, b_1, p_2, Q_5
  72. Polygon(O_1, P_1, 3) → poly6, q_4, r_2, s_2, R_1
  73. Intersect(i_1, j_1) → F_1
  74. Intersect(b, j_1) → I_1
  75. Intersect(i_1, l_1) → J_1
  76. Circle(I_1, 0.3) → d_4
  77. Circle(F_1, 0.3) → d_7
  78. Circle(J_1, 0.3) → d_8
  79. Polygon(N_4, N_1, N_2, N_3) → poly7, n_5, n_6, n_7, n_8
  80. Polygon(M_1, M_2, M_3, M_4) → poly8, m_3, m_4, m_5, m_6
  81. Polygon(U_1, V_1, 4) → poly9, p_1, s_1, t_1, f_{13}, W_1, Z_1
  82. Polygon(U_1, V_1, 4) → poly10, g_2, t_2, a_2, b_2, A_2, B_2
  83. Polygon(Q_1, Q_2, 4) → poly11, r_1, e_{10}, e_{12}, f_{11}, Q, I_2
  84. Polygon(C_2, D_2, 3) → poly12, q_1, q_2, b_3, B_3
  85. Polygon(D_3, C_3, 3) → poly14, i_4, j_4, l_4, E_3
  86. Polygon(Q_1, Q_2, Q_3, Q_4) → poly13, q_3, q_5, q_6, q_7
  87. Circle(Q_1, 0.5) → e_{11}
  88. Intersect(e_{11}, q_7) → J_2,
  89. Intersect(e_{11}, q_3) → K_2,
  90. Circle(K_2, 1) → g_3
  91. Intersect(g_3, q_3) → O_2,
  92. Circle(O_2, 1) → h_3
  93. Intersect(h_3, q_3) → P_2, R_2
  94. Circle(J_2, 1) → k_3
  95. Intersect(k_3, q_7) → S_2,
  96. Circle(S_2, 1) → p_3
  97. Intersect(p_3, q_7) → T_2, U_2
  98. OrthogonalLine(T_2, q_7) → i_3
  99. OrthogonalLine(S_2, q_7) → j_3
  100. OrthogonalLine(J_2, q_7) → l_3
  101. OrthogonalLine(K_2, q_3) → r_3
  102. OrthogonalLine(O_2, q_3) → s_3
  103. OrthogonalLine(R_2, q_3) → t_3
  104. OrthogonalLine(J_2, r_3) → a_3
  105. OrthogonalLine(S_2, r_3) → f_{14}
  106. OrthogonalLine(T_2, r_3) → g_4
  107. Intersect(r_3, g_4) → V_2
  108. Intersect(s_3, g_4) → W_2
  109. Intersect(t_3, g_4) → Z_2
  110. Intersect(t_3, f_{14}) → A_3
  111. Intersect(s_3, f_{14}) → F_3
  112. Intersect(r_3, f_{14}) → G_3
  113. Intersect(r_3, a_3) → H_3
  114. Intersect(s_3, a_3) → I_3
  115. Intersect(t_3, a_3) → J_3
  116. Circle(V_2, 0.3) → e_1
  117. Circle(W_2, 0.3) → e_2
  118. Circle(Z_2, 0.3) → e_3
  119. Circle(G_3, 0.3) → e_4
  120. Circle(F_3, 0.3) → e_5
  121. Circle(A_3, 0.3) → e_6
  122. Circle(H_3, 0.3) → e_7
  123. Circle(I_3, 0.3) → e_8
  124. Circle(J_3, 0.3) → e_9
  125. Polygon(K_3, O_3, 3) → poly15, h_4, k_4, p_4, P_3
  126. Polygon(S_3, R_3, 3) → poly16, r_4, s_4, t_4, T_3
  127. Polygon(L_4, L_1, L_2, L_3) → poly17, l_5, l_6, l_7, l_8
  128. Polygon(L_3, L_4, L_1, L_2) → poly18, l_9, l_{10}, l_{11}, l_{12}
  129. Circle(L_4, 0.5) → f_{10}
  130. Intersect(f_{10}, l_9) → U_3,
  131. Intersect(q_3, l_{10}) → V_3
  132. Intersect(q_3, l_{10}) → W_3
  133. Intersect(f_{10}, l_{10}) → Z_3,
  134. Circle(Z_3, 1) → g_5
  135. Intersect(g_5, l_{10}) → A_4,
  136. Circle(A_4, 1) → h_5
  137. Intersect(h_5, l_{10}) → B_4, C_4
  138. Circle(U_3, 1) → k_5
  139. Intersect(k_5, l_9) → D_4,
  140. Circle(D_4, 1) → p_5
  141. Intersect(p_5, l_9, 1) → E_4
  142. OrthogonalLine(E_4, l_9) → a_4
  143. OrthogonalLine(D_4, l_9) → b_4
  144. OrthogonalLine(U_3, l_9) → i_5
  145. OrthogonalLine(Z_3, l_{10}) → j_5
  146. OrthogonalLine(A_4, l_{10}) → r_5
  147. OrthogonalLine(C_4, l_{10}) → s_5
  148. Intersect(a_4, j_5) → F_4
  149. Intersect(b_4, j_5) → G_4
  150. Intersect(i_5, j_5) → H_4
  151. Intersect(i_5, r_5) → I_4
  152. Intersect(b_4, r_5) → J_4
  153. Intersect(a_4, r_5) → K_4
  154. Intersect(a_4, s_5) → O_4
  155. Intersect(b_4, s_5) → P_4
  156. Intersect(i_5, s_5) → R_4
  157. Circle(H_4, 0.3) → f_1
  158. Circle(G_4, 0.3) → f_2
  159. Circle(F_4, 0.3) → f_3
  160. Circle(I_4, 0.3) → f_4
  161. Circle(J_4, 0.3) → f_5
  162. Circle(K_4, 0.3) → f_6
  163. Circle(R_4, 0.3) → f_7
  164. Circle(P_4, 0.3) → f_8
  165. Circle(O_4, 0.3) → f_9
  166. Circle(E, 0.6) → t_5