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Squares and Square Roots

Squares and Square Roots
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2016-09-24 23:32
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the geometric representation and relationship between squares and square roots. It involves core mathematical concepts such as square operations, square roots, real numbers, ratios, scalene triangles, Pythagorean theorem, and spheres. Construction highlights include commands like Shuffle, Element, Random, Midpoint, Polygon, LaTeX, Textfield, Segment, Point, and Ellipse. Suitable for middle school and above students to understand the geometric meaning and practical applications of square roots.

GeoGebra Commands & Parameters

  1. Shuffle({2, 4, 6, 8, 10, 12}) → list1
  2. Element(list1, 2) → j
  3. Element(list1, 1) → e
  4. Random(13, 20) → f_2
  5. Random(3, 12) → v_1
  6. Random(13, 20) → e_2
  7. Random(3, 12) → w_1
  8. Element(Words, l) → text73
  9. Element(Words, j) → text8
  10. Element(Words, e) → text7
  11. Element(Words, k) → text9
  12. Element(list1, 4) → l_3
  13. Element(Words, l_3) → text10
  14. Element(Words, k) → text72
  15. Midpoint(B, D) → H
  16. Midpoint(A, C) → F
  17. Midpoint(F, H) → I
  18. Midpoint(I, H) → R
  19. Midpoint(M_1, N_1) → O_1
  20. Midpoint(O_1, N_1) → Q_1
  21. Midpoint(M_1, O_1) → P_1
  22. Midpoint(F, I) → M
  23. Midpoint(A, B) → E
  24. Midpoint(C, D) → G
  25. Midpoint(E, I) → J
  26. Midpoint(A, F) → K
  27. Midpoint(B, H) → L
  28. Midpoint(K, J) → N
  29. Midpoint(A, E) → O
  30. Midpoint(E, B) → P
  31. Midpoint(J, L) → Q
  32. Midpoint(C, G) → S
  33. Midpoint(G, D) → T
  34. Polygon(U, V, W, Z) → poly1, u, v, w, z_1
  35. Polygon(A_1, B_1, C_1, D_1) → poly2, a_1, b_1, c_1, d_1
  36. Polygon(E_1, F_1, G_1, H_1) → poly3, e_1, f_1, g_1, h_1
  37. Polygon(F, M, P_1, M_1) → poly5, f, m, s, n_1
  38. Polygon(I_1, J_1, K_1, L_1) → poly4, i_1, j_1, k_1, l_1
  39. Polygon(I, R, Q_1, O_1) → poly7, r, t, q_1, s_1
  40. Polygon(M, I, O_1, P_1) → poly6, g, i, m_1, p_1
  41. Polygon(R, H, N_1, Q_1) → poly8, h, r_1, t_1, a_2
  42. Element(list1, 3) → k_3
  43. Shuffle({1, 2, 3, 4}) → Mix
  44. Element(Mix, 1) → n
  45. Element(Mix, 2) → o
  46. Element(Mix, 3) → p
  47. Element(Mix, 4) → q
  48. Element(ShownWords, n) → text11
  49. Element(ShownWords, o) → text12
  50. Element(ShownWords, p) → text13
  51. Element(ShownWords, q) → text14
  52. Element(Definitions, e) → text21
  53. Element(Definitions, j) → text22
  54. LaTeX(Points, true, true) → text25
  55. Polygon(K, M_1, P_1, N) → poly9, k_2, m_2, p_2, n_2
  56. Polygon(N, J, O_1, P_1) → poly10, n_3, j_2, o_1, p_3
  57. Polygon(J, O_1, Q_1, Q) → poly11, j_3, o_2, q_2, q_3
  58. Polygon(Q, Q_1, N_1, L) → poly12, q_4, q_5, n_4, l_2
  59. Textfield(Name) → inputBox1
  60. Textfield(Date) → inputBox2
  61. Segment(R_1, S_1) → b_2
  62. Point(b_2) → T_1
  63. Ellipse(U_1, V_1, T_1) → c_2
  64. Point(c_2) → W_1
  65. Point(c_2) → Z_1
  66. Segment(C_2, D_2) → d_2
  67. Point(d_2) → E_2
  68. Element(Definitions, k) → text23
  69. Element(Definitions, l) → text24