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棋盘上的正方形计数

棋盘上的正方形计数
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2019-11-05 16:53
函数解析几何几何作图
①本范例演示如何在棋盘上系统性地计数正方形；②涉及的核心数学概念包括组合数学、计数原理和正方形面积计算；③作图要点——从下方『构造摘要』提炼用到了 Point（点）、Max（最大值）、Polygon（多边形）、Segment（线段）等 GeoGebra 命令/对象；④适合初中及以上学段，用于教学演示或数学思维训练。

GeoGebra 命令及参数

  1. Point(xAxis) → C
  2. Point(yAxis) → E
  3. Max(a, b) → largest
  4. Polygon(B, A, 4) → poly1, f, g, h, i, F, G
  5. Point(xAxis) → H
  6. Segment(H, E) → j
  7. Segment(H, C) → k
  8. Segment(C, D) → l
  9. Segment(D, E) → m
  10. Point(k) → I
  11. Point(k) → J
  12. Point(j) → K
  13. Polygon(L, K, 4) → poly2, n, p, q, r, M, N
  14. Polygon(J, I, 4) → poly3, s, t, d, e, O, P
  15. Point(k) → Q
  16. Point(k) → R
  17. Point(k) → T
  18. Point(k) → U
  19. Polygon(Q, R, 4) → poly4, f_1, g_1, h_1, i_1, V, W
  20. Polygon(V, P, 4) → poly5, j_1, k_1, l_1, m_1, Z, A_1
  21. Polygon(S, T, 4) → poly6, n_1, p_1, q_1, r_1, B_1, C_1
  22. Polygon(C, U, 4) → poly7, s_1, t_1, a_1, b_1, D_1, E_1
  23. Polygon(D_1, C_1, 4) → poly8, c_1, d_1, e_1, f_2, F_1, G_1
  24. Polygon(B_1, W, 4) → poly9, g_2, h_2, i_2, j_2, H_1, I_1
  25. Polygon(Z, N, 4) → poly10, k_2, l_2, m_2, n_2, J_1, K_1
  26. Polygon(H_1, A_1, 4) → poly11, p_2, q_2, r_2, s_2, L_1, M_1
  27. Polygon(F_1, I_1, 4) → poly12, t_2, a_2, b_2, c_2, N_1, O_1
  28. Point(l) → P_1
  29. Polygon(P_1, G_1, 4) → poly13, d_2, e_2, f_3, g_3, Q_1, R_1
  30. Point(j) → S_1
  31. Polygon(J_1, S_1, 4) → poly14, h_3, i_3, j_3, k_3, T_1, U_1
  32. Polygon(L_1, K_1, 4) → poly15, l_3, m_3, n_3, p_3, V_1, W_1
  33. Polygon(N_1, M_1, 4) → poly16, q_3, r_3, s_3, t_3, Z_1, A_2
  34. Polygon(Q_1, O_1, 4) → poly17, a_3, b_3, c_3, d_3, B_2, C_2
  35. Point(l) → D_2
  36. Polygon(V_1, U_1, 4) → poly18, e_3, f_4, g_4, h_4, E_2, F_2
  37. Polygon(Z_1, W_1, 4) → poly19, i_4, j_4, k_4, l_4, G_2, H_2
  38. Polygon(B_2, A_2, 4) → poly20, m_4, n_4, p_4, q_4, I_2, J_2
  39. Polygon(D_2, C_2, 4) → poly21, r_4, s_4, t_4, a_4, K_2, L_2
  40. Polygon(K_2, J_2, 4) → poly22, b_4, c_4, d_4, e_4, M_2, N_2
  41. Polygon(I_2, H_2, 4) → poly23, f_5, g_5, h_5, i_5, O_2, P_2
  42. Polygon(G_2, F_2, 4) → poly24, j_5, k_5, l_5, m_5, Q_2, R_2
  43. Point(j) → S_2
  44. Polygon(E_2, S_2, 4) → poly25, n_5, p_5, q_5, r_5, T_2, U_2
  45. Point(l) → V_2
  46. Polygon(V_2, N_2, 4) → poly26, s_5, t_5, a_5, b_5, W_2, Z_2
  47. Polygon(M_2, P_2, 4) → poly27, c_5, d_5, e_5, f_6, A_3, B_3
  48. Polygon(O_2, R_2, 4) → poly28, g_6, h_6, i_6, j_6, C_3, D_3
  49. Polygon(Q_2, U_2, 4) → poly29, k_6, l_6, m_6, n_6, E_3, F_3
  50. Point(j) → G_3
  51. Polygon(W_2, B_3, 4) → poly30, p_6, q_6, r_6, s_6, H_3, I_3
  52. Polygon(A_3, D_3, 4) → poly31, t_6, a_6, b_6, c_6, J_3, K_3
  53. Polygon(C_3, F_3, 4) → poly32, d_6, e_6, f_7, g_7, L_3, M_3
  54. Polygon(E_3, G_3, 4) → poly33, h_7, i_7, j_7, k_7, N_3, O_3