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Square and Hexagon

Square and Hexagon
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2019-03-21 00:44
PolygonTransformationGeometric Construction
In collections Cutting up squares
This example demonstrates the geometric construction of a square and a hexagon. It involves the basic properties of regular polygons. Using GeoGebra commands such as Polygon, Rotate, and Translate, you can dynamically construct a square and a hexagon. Suitable for students at the middle school level and above to learn geometric construction and the basic properties of polygons.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, yAxis) → b
  2. Point(b) → B
  3. Polygon(A, B, 6) → poly1, a_1, F, b_1, c, d, e, f, C, D, E
  4. Segment(F, C) → p
  5. Midpoint(b_1) → N
  6. Rotate(A, 180°, N) → A'
  7. Rotate(F, 180°, N) → F'
  8. Rotate(C, 180°, N) → C'
  9. Rotate(B, 180°, N) → B'
  10. Vector(A, F') → w
  11. Translate(A, w) → A'_1
  12. Translate(F, w) → F'_1
  13. Translate(C, w) → C'_1
  14. Translate(B, w) → B'_1
  15. Translate(A'_1, w) → O
  16. Translate(F'_1, w) → P
  17. Translate(C'_1, w) → Q
  18. Translate(B'_1, w) → R
  19. Translate(A', w) → A''
  20. Translate(F', w) → F''
  21. Translate(C', w) → C''
  22. Translate(B', w) → B''
  23. Translate(A'', w) → A'''
  24. Translate(F'', w) → F'''
  25. Translate(C'', w) → C'''
  26. Translate(B'', w) → B'''
  27. Translate(O, w) → O'
  28. Translate(P, w) → P'
  29. Translate(Q, w) → Q'
  30. Translate(R, w) → R'
  31. Intersect(e, f) → S
  32. Intersect(c, d) → T
  33. Intersect(c, e) → U
  34. Intersect(d, e) → V
  35. Intersect(c, b_1) → W
  36. Polygon(S, W, B, A) → poly2, s, w_1, b_2, a_2
  37. Midpoint(w_1) → Z
  38. Rotate(S, 180°, Z) → S'
  39. Rotate(W, 180°, Z) → W'
  40. Rotate(B, 180°, Z) → B'_2
  41. Rotate(A, 180°, Z) → A'_2
  42. Polygon(S', W', B'_2, A'_2) → poly2', s', w', b'_2, a'_2
  43. Midpoint(a'_2) → A_1
  44. Rotate(S', 180°, A_1) → S''
  45. Rotate(W', 180°, A_1) → W''
  46. Rotate(B'_2, 180°, A_1) → B_1
  47. Rotate(A'_2, 180°, A_1) → C_1
  48. Polygon(S'', W'', B_1, C_1) → poly2'', s'', w'', b_3, c_1
  49. Midpoint(w'') → D_1
  50. Rotate(S'', 180°, D_1) → S'''
  51. Rotate(W'', 180°, D_1) → W'''
  52. Rotate(B_1, 180°, D_1) → E_1
  53. Rotate(C_1, 180°, D_1) → F_1
  54. Polygon(S''', W''', E_1, F_1) → poly2''', s''', w''', e_1, f_1
  55. Midpoint(f_1) → G_1
  56. Rotate(S''', 180°, G_1) → H_1
  57. Rotate(W''', 180°, G_1) → I_1
  58. Rotate(E_1, 180°, G_1) → J_1
  59. Rotate(F_1, 180°, G_1) → K_1
  60. Intersect(w_1, w') → R_1
  61. Intersect(w_1, w') → S_1
  62. Intersect(a'_2, b'_2) → V_1
  63. Intersect(a'_2, s') → W_1
  64. Intersect(w'', s'') → B_2
  65. Intersect(b_2, w_1) → D_2
  66. Intersect(b_3, w'') → E_2
  67. Intersect(w_1, s) → F_2
  68. Line(D_2, G) → h
  69. OrthogonalLine(G, h) → i
  70. Circle(G, sqrt(poly1)) → k
  71. Intersect(k, i) → H, I
  72. Intersect(k, h) → J, K
  73. OrthogonalLine(J, h) → g
  74. OrthogonalLine(K, h) → j
  75. OrthogonalLine(H, i) → m
  76. Circle(H, sqrt(poly1)) → q
  77. Intersect(q, i, 2) → N_1
  78. OrthogonalLine(N_1, i) → g_1
  79. Intersect(g, g_1) → O_1
  80. Circle(O_1, sqrt(poly1)) → p_1
  81. Intersect(p_1, g, 1) → P_1
  82. Intersect(p_1, g_1, 2) → Q_1
  83. OrthogonalLine(P_1, g) → l_1
  84. OrthogonalLine(Q_1, g_1) → m_1
  85. Intersect(h, b'_2) → T_1
  86. Intersect(h, m_1) → U_1
  87. Intersect(m_1, s') → Z_1
  88. Intersect(g, s'') → A_2
  89. Intersect(h, g) → C_2
  90. Intersect(m, m_1) → G_2
  91. Intersect(m, g) → H_2
  92. Polygon(E_2, B_2, A_2) → poly4, a_3, e_2, b_4
  93. Polygon(A_2, E_2, W_1, V_1) → poly5, a_4, e_3, w_2, v_1
  94. Polygon(C_2, A_2, T_1) → poly6, t_1, c_2, a_5
  95. Polygon(W_1, V_1, T_1, U_1, Z_1) → poly7, w_3, v_2, t_2, u_1, z_1
  96. Intersect(m, i) → I_2
  97. Polygon(I_2, B_2, E_2) → poly8, e_4, i_2, b_5
  98. Vector(I_2, E_2) → u
  99. Translate(E_2, u) → J_2
  100. Translate(B_2, u) → K_2
  101. Translate(A_2, u) → L_2
  102. Polygon(J_2, K_2, L_2) → poly4', l_2, j_2, k_2
  103. Translate(I_2, u) → M_2
  104. Translate(B_2, u) → N_2
  105. Translate(E_2, u) → O_2
  106. Polygon(M_2, N_2, O_2) → poly8', o_2, m_2, n_2
  107. Vector(W_1, B_2) → v
  108. Translate(W_1, v) → P_2
  109. Translate(V_1, v) → Q_2
  110. Translate(T_1, v) → R_2
  111. Translate(U_1, v) → S_2
  112. Translate(Z_1, v) → T_2
  113. Polygon(P_2, Q_2, R_2, S_2, T_2) → poly7', p_2, q_2, r_2, s_2, t_3
  114. Vector(C_2, S_2) → z
  115. Translate(C_2, z) → U_2
  116. Translate(A_2, z) → V_2
  117. Translate(T_1, z) → W_2
  118. Polygon(U_2, V_2, W_2) → poly6', w_4, u_2, v_3
  119. Vector(I_2, R_2) → z_2
  120. Translate(I_2, z_2) → Z_2
  121. Translate(B_2, z_2) → A_3
  122. Translate(E_2, z_2) → B_3
  123. Polygon(Z_2, A_3, B_3) → poly8'_1, b_6, z_3, a_6
  124. Intersect(h, m_1) → L
  125. Intersect(h, w_1) → M
  126. Intersect(m_1, s') → L_1
  127. Polygon(L, L_1, M) → poly3, m_3, l_3, l_4