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Sum Numbers, Squares, Lines & Dots_Tens

Sum Numbers, Squares, Lines & Dots_Tens
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2017-05-23 00:29
SequenceCoordinate GeometryCalculusGraphing
This example demonstrates how to construct and sum combinations of numbers, squares, lines, and dots using GeoGebra. It involves core mathematical concepts such as sequences, geometric constructions, coordinate geometry, and calculus concepts like derivatives and integrals. Key GeoGebra commands and objects used in the construction include Sequence, Point, Polygon, Random, RotateText, Ellipse, Segment, and Textfield. Suitable for high school and above, it illustrates the integration of geometric shapes with algebraic operations and the power of dynamic geometry.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 0, 9], j, 1, 10) → list1
  2. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 11, 20], j, 1, 10) → list2
  3. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 11, 20], j, 12, 21) → list4
  4. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 0, 9], j, 12, 21) → list5
  5. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 0, 9], j, 23, 32) → list6
  6. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 11, 20], j, 23, 32) → list8
  7. Sequence(Polygon[(35, i), (35, i + 1), 4], i, 0, 9) → list12
  8. Sequence(Polygon[(37, i), (37, i + 1), 4], i, 0, 9) → list13
  9. Sequence(Polygon[(39, i), (39, i + 1), 4], i, 0, 9) → list14
  10. Sequence(Polygon[(39, i), (39, i + 1), 4], i, 11, 20) → list19
  11. Sequence(Polygon[(37, i), (37, i + 1), 4], i, 11, 20) → list20
  12. Sequence(Polygon[(35, i), (35, i + 1), 4], i, 11, 20) → list21
  13. Sequence((i, 23), i, 42, 60, 2) → list24
  14. Point(list24) → A
  15. Point(list24) → B
  16. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  17. Point(list24) → E
  18. Point(list24) → F
  19. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
  20. Point(list24) → I
  21. Point(list24) → J
  22. Polygon(I, J, 4) → poly3, n, p, q, r, K, L
  23. Point(list24) → M
  24. Point(list24) → N
  25. Polygon(M, N, 4) → poly4, s, t, a, b, O, P
  26. Point(list24) → Q
  27. Point(list24) → R
  28. Polygon(Q, R, 4) → poly5, c, d, e, f_1, S, T
  29. Sequence((i, 27), i, 42, 60, 2) → list25
  30. Point(list25) → U
  31. Point(list25) → V
  32. Polygon(U, V, 4) → poly6, g_1, h_1, i_1, j_1, W, Z
  33. Point(list25) → A_1
  34. Point(list25) → B_1
  35. Polygon(A_1, B_1, 4) → poly7, k_1, l_1, m_1, n_1, C_1, D_1
  36. Point(list25) → E_1
  37. Point(list25) → F_1
  38. Polygon(E_1, F_1, 4) → poly8, p_1, q_1, r_1, s_1, G_1, H_1
  39. Point(list25) → I_1
  40. Point(list25) → J_1
  41. Polygon(I_1, J_1, 4) → poly9, t_1, a_1, b_1, c_1, K_1, L_1
  42. Point(list25) → M_1
  43. Point(list25) → N_1
  44. Polygon(M_1, N_1, 4) → poly10, d_1, e_1, f_2, g_2, O_1, P_1
  45. Sequence(Polygon[(35, i), (35, i + 1), 4], i, 22, 31) → list18
  46. Sequence(Polygon[(37, i), (37, i + 1), 4], i, 22, 31) → list17
  47. Sequence(Polygon[(39, i), (39, i + 1), 4], i, 22, 31) → list15
  48. Point(list25) → Q_1
  49. Point(list25) → R_1
  50. Polygon(Q_1, R_1, 4) → poly11, h_2, i_2, j_2, k_2, S_1, T_1
  51. Point(list24) → U_1
  52. Point(list24) → V_1
  53. Polygon(U_1, V_1, 4) → poly12, l_2, m_2, n_2, p_2, W_1, Z_1
  54. Random(1, 9) → rhund
  55. Random(0, 9) → rten
  56. Random(0, 9) → rone
  57. Sequence(Sequence[Polygon[(i, j), (i + 4, j), 4], i, 41, 60, 4], j, 22, 26, 4) → list23
  58. RotateText(text4, 45°) → text10
  59. RotateText(text5, 45°) → text11
  60. RotateText(text6, 45°) → text12
  61. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 22, 31], j, 1, 10) → list3
  62. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 22, 31], j, 12, 21) → list10
  63. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 22, 31], j, 23, 32) → list11
  64. Ellipse(A_2, B_2, C_2) → c_2
  65. Polygon(D_2, E_2, F_2, G_2) → poly13, d_2, e_2, f_3, g_3
  66. Point(g_3) → H_2
  67. Point(e_2) → I_2
  68. Segment(H_2, I_2) → q_2
  69. Textfield(YourGuess) → InputBox1