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n个整数求和演示

n个整数求和演示
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2016-09-27 23:45
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①本范例演示了n个整数的求和图形化表示；②涉及的核心数学概念包括整数求和、滑动求和、矩形构造；③作图要点——从下方『构造摘要』提炼用到了Point, Polygon, Rotate等GeoGebra命令/对象；④适合初中及以上数学学习者理解求和公式的几何意义及动态变化。

GeoGebra 命令及参数

  1. Point(yAxis) → E
  2. Polygon(E, F, 4) → poly2, e, f, g, h, G, H
  3. Polygon(F, I, 4) → poly3, i, j, k, l, J, K
  4. Point(yAxis) → L
  5. Polygon(L, M, 4) → poly4, m, p, q, r, N, O
  6. Polygon(M, P, 4) → poly5, s, t, a_1, b_1, Q, R
  7. Polygon(P, S, 4) → poly6, c_1, d_1, e_1, f_1, T, U
  8. Point(yAxis) → V
  9. Polygon(V, W, 4) → poly7, g_1, h_1, i_1, j_1, Z, A_1
  10. Polygon(W, B_1, 4) → poly8, k_1, l_1, m_1, n_1, C_1, D_1
  11. Polygon(B_1, E_1, 4) → poly9, p_1, q_1, r_1, s_1, F_1, G_1
  12. Polygon(E_1, H_1, 4) → poly10, t_1, a_2, b_2, c_2, I_1, J_1
  13. Point(yAxis) → K_1
  14. Polygon(K_1, L_1, 4) → poly11, d_2, e_2, f_2, g_2, M_1, N_1
  15. Polygon(L_1, O_1, 4) → poly12, h_2, i_2, j_2, k_2, P_1, Q_1
  16. Polygon(O_1, R_1, 4) → poly13, l_2, m_2, n_2, p_2, S_1, T_1
  17. Polygon(R_1, U_1, 4) → poly14, q_2, r_2, s_2, t_2, V_1, W_1
  18. Polygon(U_1, Z_1, 4) → poly15, a_3, b_3, c_3, d_3, A_2, B_2
  19. Point(yAxis) → C_2
  20. Polygon(C_2, D_2, 4) → poly16, e_3, f_3, g_3, h_3, E_2, F_2
  21. Polygon(D_2, G_2, 4) → poly17, i_3, j_3, k_3, l_3, H_2, I_2
  22. Polygon(G_2, J_2, 4) → poly18, m_3, n_3, p_3, q_3, K_2, L_2
  23. Polygon(J_2, M_2, 4) → poly19, r_3, s_3, t_3, a_4, N_2, O_2
  24. Polygon(M_2, P_2, 4) → poly20, b_4, c_4, d_4, e_4, Q_2, R_2
  25. Polygon(H, G, 4) → poly1, a, b, c, d, A, C
  26. Rotate(poly1, α, RP) → poly1'
  27. Rotate(poly2, α, RP) → poly2'
  28. Rotate(poly3, α, RP) → poly3'
  29. Rotate(poly4, α, RP) → poly4'
  30. Rotate(poly5, α, RP) → poly5'
  31. Rotate(poly6, α, RP) → poly6'
  32. Rotate(poly7, α, RP) → poly7'
  33. Rotate(poly8, α, RP) → poly8'
  34. Rotate(poly9, α, RP) → poly9'
  35. Rotate(poly11, α, RP) → poly11'
  36. Rotate(poly12, α, RP) → poly12'
  37. Rotate(poly13, α, RP) → poly13'
  38. Rotate(poly14, α, RP) → poly14'
  39. Rotate(poly15, α, RP) → poly15'
  40. Rotate(poly16, α, RP) → poly16'
  41. Rotate(poly17, α, RP) → poly17'
  42. Rotate(poly18, α, RP) → poly18'
  43. Rotate(poly19, α, RP) → poly19'
  44. Polygon(P_2, S_2, 4) → poly21, f_4, g_4, h_4, i_4, D, T_2
  45. Rotate(poly21, α, RP) → poly21'
  46. Rotate(poly20, α, RP) → poly20'
  47. Rotate(poly10, α, RP) → poly10'