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Play Chomp! – An Interactive Strategy Game with Geometric Construction

Play Chomp! – An Interactive Strategy Game with Geometric Construction
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2017-11-29 08:20
PolygonSequenceTransformationInequalityGeometric Construction
① This example demonstrates the classic strategy game 'Chomp', where players click cells to remove upper-right regions, aiming to force the opponent to take the poisoned square. ② Core mathematical concepts include game theory winning strategies, set theory subset relations, and geometric transformations involving symmetry and position; it also incorporates equilateral triangles, circles, and ratios to construct the board and interactive elements. ③ Construction highlights: GeoGebra commands such as Random for random initial setups, Intersect and Point for key locations, Polygon for board regions, and Sequence for batch-generating cell objects; objects include l, t, A, B, p11–p15, with auxiliary objects f, g, h, etc., enabling dynamic interaction. ④ Suitable for middle school and above, this example serves math game teaching, introductory game theory, geometric and logical thinking training, and as an exploratory case combining programming with mathematics.

GeoGebra Commands & Parameters

  1. Random(5, 10) → l
  2. Random(3, 5) → t
  3. Intersect(xAxis, yAxis) → A
  4. Polygon(A, B, 4) → p11, f, g, h, i, C, D
  5. Point(xAxis) → E
  6. Polygon(B, E, 4) → p12, j, k, m, n, F, G
  7. Point(xAxis) → H
  8. Polygon(E, H, 4) → p13, p, q, r, s, I, J
  9. Point(xAxis) → K
  10. Polygon(H, K, 4) → p14, a, b, c, d, L, M
  11. Point(xAxis) → N
  12. Polygon(K, N, 4) → p15, e, f_1, g_1, h_1, O, P
  13. Point(xAxis) → Q
  14. Polygon(N, Q, 4) → p16, i_1, j_1, k_1, l_1, R, S
  15. Point(xAxis) → T
  16. Polygon(Q, T, 4) → p17, m_1, n_1, p_1, q_1, U, V
  17. Polygon(T, W, 4) → p18, r_1, s_1, t_1, a_1, Z, A_1
  18. Polygon(D, C, 4) → p21, b_1, c_1, d_1, e_1, B_1, C_1
  19. Polygon(C, F, 4) → p22, f_2, g_2, h_2, i_2, D_1, E_1
  20. Polygon(F, I, 4) → p23, j_2, k_2, l_2, m_2, F_1, G_1
  21. Polygon(I, L, 4) → p24, n_2, p_2, q_2, r_2, H_1, I_1
  22. Polygon(L, O, 4) → p25, s_2, t_2, a_2, b_2, J_1, K_1
  23. Polygon(O, R, 4) → p26, c_2, d_2, e_2, f_3, L_1, M_1
  24. Polygon(R, U, 4) → p27, g_3, h_3, i_3, j_3, N_1, O_1
  25. Polygon(U, Z, 4) → p28, k_3, l_3, m_3, n_3, P_1, Q_1
  26. Polygon(C_1, B_1, 4) → p31, p_3, q_3, r_3, s_3, R_1, S_1
  27. Polygon(B_1, D_1, 4) → p32, t_3, a_3, b_3, c_3, T_1, U_1
  28. Polygon(D_1, F_1, 4) → p33, d_3, e_3, f_4, g_4, V_1, W_1
  29. Polygon(F_1, H_1, 4) → p34, h_4, i_4, j_4, k_4, Z_1, A_2
  30. Polygon(H_1, J_1, 4) → p35, l_4, m_4, n_4, p_4, B_2, C_2
  31. Polygon(J_1, L_1, 4) → p36, q_4, r_4, s_4, t_4, D_2, E_2
  32. Polygon(L_1, N_1, 4) → p37, a_4, b_4, c_4, d_4, F_2, G_2
  33. Polygon(N_1, P_1, 4) → p38, e_4, f_5, g_5, h_5, H_2, I_2
  34. Sequence(Segment[(a, 0), (a, 3)], a, 0, 8) → L_2
  35. Sequence(Segment[(0, a), (8, a)], a, 0, 3) → L_3