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Hexagon Dimensions

Hexagon Dimensions
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2018-02-26 18:04
PolygonTransformationGeometric Construction
In collections Folding paper, doing geometry figures
This example demonstrates the geometric construction and dimension calculation of a hexagon. It involves core mathematical concepts such as polygon construction, midpoint, rotation, arc intersection, angle bisector, perpendicular line, and mirror. GeoGebra commands used include Polygon, Segment, Midpoint, Rotate, CircleArc, Intersect, AngularBisector, OrthogonalLine, Mirror, Circle, and Line. It is suitable for high school geometry construction teaching and learning, helping to understand polygon properties and construction methods.

GeoGebra Commands & Parameters

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Segment((sqrt(2) / 4, 0), (sqrt(2) / 4, 1)) → f
  3. Segment((sqrt(2) / 2, 0), (sqrt(2) / 2, 1)) → g
  4. Segment(((3 * sqrt(2) / 4), 0), ((3 * sqrt(2) / 4), 1)) → h
  5. Midpoint(B, D) → E
  6. Rotate(D, -90°, E) → DD
  7. CircleArc(E, DD, D) → e
  8. Intersect(e, h, 1) → F
  9. CircleArc(E, F, D) → k
  10. AngularBisector(F, E, D) → i
  11. Intersect(i, c) → G
  12. Segment(E, G) → j
  13. Polygon(A, C, G, E, B) → veelhoek1, a_1, c_1, g_1, e_1, b_1
  14. Polygon(E, D, G) → driehoek1, g_2, e_2, d_1
  15. Rotate(E, (((-(s - 1)) * 180))°, g_1) → E'
  16. Rotate(D, (((-(s - 1)) * 180))°, g_1) → D'
  17. Rotate(G, (((-(s - 1)) * 180))°, g_1) → G'
  18. Polygon(E', D', G') → driehoek1', g', e', d'
  19. Polygon(E, F, G) → driehoek2, g_3, e_3, f_1
  20. Segment(E, D) → l
  21. Segment(D, G) → m
  22. OrthogonalLine(F, a_1) → n
  23. Intersect(j, d') → II
  24. Intersect(n, j) → R
  25. Intersect(n, a_1) → S
  26. Segment(R, S) → p
  27. Segment(F, S) → q
  28. Mirror(F, g) → H
  29. Mirror(G, g) → I
  30. Segment(I, E) → r
  31. CircleArc(E, B, H) → t
  32. Polygon(I, E, B) → driehoek3, b_2, i_1, e_4
  33. Rotate(I, (((s - 3) * 180))°, r) → I'
  34. Rotate(E, (((s - 3) * 180))°, r) → E'_1
  35. Rotate(B, (((s - 3) * 180))°, r) → B'
  36. Polygon(I', E'_1, B') → driehoek3', b', i', e'_1
  37. Polygon(E, I, A, C, G) → veelhoek2, e_5, i_2, a_2, c_2, g_4
  38. Segment(B, E) → h_1
  39. Segment(B, I) → j_1
  40. Mirror(R, g) → TT
  41. Mirror(S, g) → SS
  42. Segment(SS, TT) → k_1
  43. Segment(SS, H) → l_1
  44. Polygon(I, H, E) → driehoek4, e_6, i_3, h_2
  45. Circle(G, C) → p_1
  46. Intersect(d', f_1) → J
  47. Intersect(d', f_1) → K
  48. Intersect(d', f_1) → L
  49. Intersect(d', f_1) → M
  50. Intersect(p_1, f_1) → N,
  51. CircleArc(G, N, C) → q_1
  52. Line(G, F) → m_1
  53. Intersect(m_1, a_2) → O
  54. Segment(O, F) → n_1
  55. Polygon(O, C, G) → driehoek5, g_5, o, c_3
  56. Rotate(O, (((s - 5) * 180))°, c_3) → O'
  57. Rotate(C, (((s - 5) * 180))°, c_3) → C'
  58. Rotate(G, (((s - 5) * 180))°, c_3) → G'_1
  59. Polygon(O', C', G'_1) → driehoek5', g'_1, o', c'
  60. Polygon(I, A, O, G, E) → veelhoek3, i_4, a_3, o_1, g_6, e_7
  61. Mirror(O, n_1) → O'_1
  62. Mirror(C, n_1) → C'_1
  63. Mirror(G, n_1) → G'_2
  64. Polygon(O'_1, C'_1, G'_2) → driehoek5'_1, g'_2, o'_1, c'_1
  65. Mirror(O, g) → O'_2
  66. Mirror(C, g) → C'_2
  67. Mirror(G, g) → G'_3
  68. Polygon(O'_2, C'_2, G'_3) → driehoek5'_2, g'_3, o'_2, c'_2
  69. Rotate(O, (((s - 5) * 180))°, c_3) → O'_3
  70. Rotate(G, (((s - 5) * 180))°, c_3) → G'_4
  71. Rotate(O'_2, (((-(s - 6)) * 180))°, c'_2) → Q
  72. Rotate(G'_3, (((-(s - 6)) * 180))°, c'_2) → U
  73. Intersect(c', o_1) → V
  74. Intersect(c', o_1) → W
  75. Intersect(c', o_1) → Z
  76. Line(I, H) → r_1
  77. Intersect(o_1, r_1) → T
  78. Segment(O, C) → s_1
  79. Segment(C, G) → t_1
  80. Polygon(I, A, O, T) → vierhoek2, i_5, a_4, o_2, t_2
  81. Rotate(I, (((-(s - 7)) * 180))°, t_2) → I'_1
  82. Rotate(A, (((-(s - 7)) * 180))°, t_2) → A'
  83. Rotate(O, (((-(s - 7)) * 180))°, t_2) → O'_4
  84. Rotate(T, (((-(s - 7)) * 180))°, t_2) → T'
  85. Polygon(I, T, G, E) → vierhoek3, i_6, t_3, g_7, e_8
  86. Segment(E, T) → f_2
  87. Segment(T, E) → j_2
  88. Intersect(Segment[O, N], j_2) → A_1
  89. Segment(A_1, E) → k_2
  90. Rotate(I, (((-(s - 7)) * 180))°, i_6) → I'_2
  91. Rotate(A, (((-(s - 7)) * 180))°, i_6) → A'_1
  92. Rotate(O, (((-(s - 7)) * 180))°, i_6) → O'_5
  93. Rotate(T, (((-(s - 7)) * 180))°, i_6) → T'_1
  94. Polygon(I'_2, A'_1, O'_5, T'_1) → vierhoek2', i'_2, a'_1, o'_5, t'_1
  95. Mirror(N, g) → NN
  96. CircleArc(I, A, NN) → d_2
  97. Segment(I, T) → l_2
  98. Intersect(g'_2, l_2) → B_1
  99. Polygon(N, B_1, T, G) → vierhoek4, n_2, b_3, t_4, g_8
  100. Segment(I, A) → m_2
  101. Segment(A, O) → p_2
  102. Mirror(H, Segment[I, G]) → HH
  103. Mirror(HH, g) → GG
  104. Intersect(n_2, g) → C_1
  105. Polygon(I, T, C_1, NN) → vierhoek5, i_7, t_5, c_4, nn
  106. Segment(HH, H) → q_2
  107. Segment(GG, F) → r_2
  108. Polygon(GG, F, G) → driehoek6, g_9, gg, f_3
  109. Polygon(I, H, HH) → driehoek7, hh, i_8, h_3
  110. Rotate(GG, (((s - 9) * 180))°, q) → GG'
  111. Rotate(F, (((s - 9) * 180))°, q) → F'
  112. Rotate(G, (((s - 9) * 180))°, q) → G'_5
  113. Polygon(GG', F', G'_5) → driehoek6', g'_5, gg', f'
  114. Rotate(I, (((s - 9) * 180))°, f) → I'_3
  115. Rotate(H, (((s - 9) * 180))°, f) → H'
  116. Rotate(HH, (((s - 9) * 180))°, f) → HH'
  117. Polygon(I'_3, H', HH') → driehoek7', hh', i'_3, h'
  118. Segment(HH, E) → s_2
  119. Segment(H, B_1) → j_3
  120. Segment(E, GG) → k_3
  121. Segment(T, F) → l_3
  122. Polygon(E, HH, H, T, F, GG) → veelhoek4, e_9, hh_1, h_4, t_6, f_4, gg_1
  123. Segment(C_1, T) → m_3
  124. Segment(E, G) → n_3
  125. Segment(T, G) → p_3
  126. Segment(T, I) → q_3
  127. Segment(E, I) → r_3
  128. Midpoint(E, T) → MM
  129. Midpoint(E, G) → HHH
  130. Midpoint(E, MM) → EM
  131. Polygon(E, MM, HHH) → driehoek8, hhh, e_{10}, mm
  132. Segment(EM, HHH) → s_3

AI Drawing Prompt Reference

Draw a regular hexagon and demonstrate its geometric construction. Start by creating base segments and points, then use rotations, midpoints, and arc intersections to form part of the hexagon. Complete the hexagon by applying angle bisectors, perpendicular lines, and reflections. Finally, add some helper lines and triangles to illustrate the symmetry and related geometric properties of the hexagon.
The prompt above was compiled from the original drawing commands and is for reference only.