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Geometric Dimensions Demonstration

Geometric Dimensions Demonstration
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2018-02-26 17:55
PolygonAngleVectorGeometric Construction
In collections Folding paper, doing geometry figures
This example demonstrates the construction and analysis of geometric dimension properties using GeoGebra. It involves core mathematical concepts such as polygons, vectors, angles, and geometric transformations. Key GeoGebra commands and objects used include Polygon, Segment, Midpoint, Rotate, CircleArc, Intersect, AngularBisector, OrthogonalLine, Mirror, Circle, Line, and Angle. Suitable for high school mathematics education to understand the construction and properties of two-dimensional figures.

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') → HH
  24. Intersect(j, d') → II
  25. Intersect(n, j) → R
  26. Intersect(n, a_1) → S
  27. Segment(R, S) → p
  28. Segment(F, S) → q
  29. Mirror(F, g) → H
  30. Mirror(G, g) → I
  31. Segment(I, E) → r
  32. CircleArc(E, B, H) → t
  33. Polygon(I, E, B) → driehoek3, b_2, i_1, e_4
  34. Rotate(I, (((s - 3) * 180))°, r) → I'
  35. Rotate(E, (((s - 3) * 180))°, r) → E'_1
  36. Rotate(B, (((s - 3) * 180))°, r) → B'
  37. Polygon(I', E'_1, B') → driehoek3', b', i', e'_1
  38. Polygon(E, I, A, C, G) → veelhoek2, e_5, i_2, a_2, c_2, g_4
  39. Segment(B, E) → h_1
  40. Segment(B, I) → j_1
  41. Mirror(R, g) → TT
  42. Mirror(S, g) → SS
  43. Segment(SS, TT) → k_1
  44. Segment(SS, H) → l_1
  45. Polygon(I, H, E) → driehoek4, e_6, i_3, h_2
  46. Circle(G, C) → p_1
  47. Intersect(d', f_1) → J
  48. Intersect(d', f_1) → K
  49. Intersect(d', f_1) → L
  50. Intersect(d', f_1) → M
  51. Intersect(p_1, f_1) → N,
  52. CircleArc(G, N, C) → q_1
  53. Line(G, F) → m_1
  54. Intersect(m_1, a_2) → O
  55. Segment(O, F) → n_1
  56. Polygon(O, C, G) → driehoek5, g_5, o, c_3
  57. Rotate(O, (((s - 5) * 180))°, c_3) → O'
  58. Rotate(C, (((s - 5) * 180))°, c_3) → C'
  59. Rotate(G, (((s - 5) * 180))°, c_3) → G'_1
  60. Polygon(O', C', G'_1) → driehoek5', g'_1, o', c'
  61. Polygon(I, A, O, G, E) → veelhoek3, i_4, a_3, o_1, g_6, e_7
  62. Mirror(O, n_1) → O'_1
  63. Mirror(C, n_1) → C'_1
  64. Mirror(G, n_1) → G'_2
  65. Polygon(O'_1, C'_1, G'_2) → driehoek5'_1, g'_2, o'_1, c'_1
  66. Mirror(O, g) → O'_2
  67. Mirror(C, g) → C'_2
  68. Mirror(G, g) → G'_3
  69. Polygon(O'_2, C'_2, G'_3) → driehoek5'_2, g'_3, o'_2, c'_2
  70. Rotate(O, (((s - 5) * 180))°, c_3) → O'_3
  71. Rotate(G, (((s - 5) * 180))°, c_3) → G'_4
  72. Rotate(O'_2, (((-(s - 6)) * 180))°, c'_2) → Q
  73. Rotate(G'_3, (((-(s - 6)) * 180))°, c'_2) → U
  74. Intersect(c', o_1) → V
  75. Intersect(c', o_1) → W
  76. Intersect(c', o_1) → Z
  77. Line(I, H) → r_1
  78. Intersect(o_1, r_1) → T
  79. Segment(O, C) → s_1
  80. Segment(C, G) → t_1
  81. Polygon(I, A, O, T) → vierhoek2, i_5, a_4, o_2, t_2
  82. Rotate(I, (((-(s - 7)) * 180))°, t_2) → I'_1
  83. Rotate(A, (((-(s - 7)) * 180))°, t_2) → A'
  84. Rotate(O, (((-(s - 7)) * 180))°, t_2) → O'_4
  85. Rotate(T, (((-(s - 7)) * 180))°, t_2) → T'
  86. Polygon(I, T, G, E) → vierhoek3, i_6, t_3, g_7, e_8
  87. Segment(E, T) → f_2
  88. Segment(T, E) → j_2
  89. Intersect(Segment[O, N], j_2) → A_1
  90. Segment(A_1, E) → k_2
  91. Rotate(I, (((-(s - 7)) * 180))°, i_6) → I'_2
  92. Rotate(A, (((-(s - 7)) * 180))°, i_6) → A'_1
  93. Rotate(O, (((-(s - 7)) * 180))°, i_6) → O'_5
  94. Rotate(T, (((-(s - 7)) * 180))°, i_6) → T'_1
  95. Polygon(I'_2, A'_1, O'_5, T'_1) → vierhoek2', i'_2, a'_1, o'_5, t'_1
  96. Mirror(N, g) → NN
  97. CircleArc(I, A, NN) → d_2
  98. Segment(I, T) → l_2
  99. Intersect(g'_2, l_2) → B_1
  100. Polygon(N, B_1, T, G) → vierhoek4, n_2, b_3, t_4, g_8
  101. Segment(I, A) → m_2
  102. Segment(A, O) → p_2
  103. Line(E, T) → q_2
  104. Line(I, G) → r_2
  105. Segment(I, E) → s_2
  106. Segment(E, G) → f_3
  107. Segment(I, T) → h_3
  108. Segment(T, G) → j_3
  109. Segment(I, G) → k_3
  110. Segment(E, T) → l_3
  111. Midpoint(E, T) → D_1
  112. Angle(G, D_1, E) → α
  113. Angle(I, D_1, T) → β
  114. Angle(T, I, E) → ι
  115. Angle(E, G, T) → κ
  116. Angle(I, E, G) → λ
  117. Angle(G, T, I) → μ
  118. Polygon(E, D_1, G) → driehoek6, g_9, e_9, d_3
  119. Angle(D_1, E, G) → γ
  120. Angle(G, D_1, E) → δ
  121. Angle(E, G, D_1) → ε
  122. Angle(G, E, D) → ζ

AI Drawing Prompt Reference

Draw a quadrilateral and two perpendicular line segments, then find their intersection point. Create an arc connecting two vertices of the quadrilateral centered at this point. Find the intersection of this arc with another line segment and draw a new arc centered at this point. Draw an angle bisector and locate its intersection with one side of the quadrilateral. Connect this intersection to a vertex to form a new pentagon. Rotate a triangle centered at the intersection point and reflect it. Finally, connect the rotated and reflected points to complete the complex shape.
The prompt above was compiled from the original drawing commands and is for reference only.