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Pentago Game Geometry

Pentago Game Geometry
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2017-09-08 07:45
PolygonGeometric ConstructionSlider Animation
This example demonstrates the geometric principles behind the Pentago game. Key mathematical concepts include geometric construction, slider animation, and locus. Using GeoGebra commands such as Polygon, Circle, Intersect, and OrthogonalLine, the game board and the trajectory of the pieces can be constructed. Suitable for middle school and above students and teachers for teaching and learning the strategies of geometric games.

GeoGebra Commands & Parameters

  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