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Sum of n Integers Demonstration

Sum of n Integers Demonstration
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2016-09-27 23:45
Geometric Construction
This example visually demonstrates the sum of n integers. Drag the n= slider to change the number of squares and the green slider to reveal the corresponding rectangle. It illustrates the concept of summing integers geometrically and dynamically, involving core math ideas like integer sums, sliding sums, and rectangle construction. Constructed using GeoGebra commands like Point, Polygon, Rotate, suitable for middle school and above to grasp the geometric meaning of sum formulas and dynamic changes.

GeoGebra Commands & Parameters

  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'