MathPlotAI Logo MathPlotAI

Tudor Arc

Tudor Arc
Loading the math board and drawing, please wait…
2023-03-17 22:25
CircleTransformationGeometric Construction
In collections geometriadinamica.es
This example demonstrates the construction of a Tudor arc. Key mathematical concepts include circle arcs and geometric construction. It uses Segment, Midpoint, Line, Circle, Intersect, Polygon, If, Rotate, CircumcircleArc, Mirror, OrthogonalLine, Vector, Translate, Point, CircleArc, Min, Arc commands in GeoGebra. Suitable for high school geometry education.

GeoGebra Commands & Parameters

  1. Segment(D, B) → e
  2. Midpoint(C, D) → F
  3. Line(F, e) → k
  4. Midpoint(F, C) → R
  5. Midpoint(R, F) → V
  6. Circle(C, V) → h_2
  7. Circle(V, C) → e_2
  8. Intersect(e_2, h_2, 2) → Z
  9. Polygon(C, Z, V) → poly1, v, c_3, z
  10. If(zz ≤ 0, 10, zz) → c
  11. Rotate(C, Max[((-(c - 2)) * 60 / (3°)), 300.00000000000006°], V) → S1_1
  12. Segment(V, S1_1) → g_2
  13. Midpoint(C, D) → E
  14. Segment(A, C) → d
  15. Rotate(C, 359.91000000000014°, E) → C''
  16. CircumcircleArc(C, C'', S1_1) → g
  17. Segment(C, F) → r
  18. Mirror(D, k) → D'_1
  19. Segment(R, S1_1) → f
  20. Segment(R, S1_1) → n_1
  21. OrthogonalLine(S1_1, g_2) → s_1
  22. Mirror(C, k) → C'
  23. Mirror(C'', k) → C'''
  24. Mirror(S1_1, k) → S1'
  25. CircumcircleArc(C', C''', S1') → g'
  26. Mirror(S1_1, k) → S1'_1
  27. Mirror(T, k) → T'
  28. Mirror(S1_1, k) → S1'_2
  29. Mirror(R, k) → R'
  30. Mirror(S1_1, k) → S1'_3
  31. Segment(R', S1'_3) → f'
  32. Mirror(C, k) → C'_3
  33. Mirror(S1_1, k) → S1'_4
  34. Mirror(V, k) → V'
  35. Midpoint(R, C) → W
  36. Mirror(C, k) → C'_4
  37. Mirror(Z, k) → Z'
  38. Mirror(V, k) → V'_1
  39. Polygon(C'_4, Z', V'_1) → poly1', v'_1, c'_4, z'
  40. Mirror(C, k) → C'_2
  41. Midpoint(C, D) → L
  42. Segment(C, L) → a_1
  43. Mirror(C, k) → C'_6
  44. Segment(T, T1) → f_2
  45. Mirror(D, f_2) → D'
  46. Mirror(B, f_2) → B'
  47. Segment(D', B') → e'
  48. Mirror(A, f_2) → A'
  49. Mirror(C, f_2) → C'_7
  50. Segment(A', C'_7) → d'
  51. Vector(A, B') → u_1
  52. Mirror(Z, k) → Z'_1
  53. Translate(pic1, u_1) → pic1'
  54. Translate(pic3, u_1) → pic3'
  55. Line(Z, V) → t_1
  56. Line(D, B) → a_2
  57. Intersect(t_1, a_2) → S
  58. Point(k) → U
  59. CircleArc(S, U, Z) → c_2
  60. Min(cc, Distance[Z, U]) → cd
  61. Circle(Z, cd) → d_2
  62. Intersect(c_2, d_2, 1) → C_1
  63. Segment(S, C_1) → b_2
  64. CircleArc(S, C_1, S1_1) → k_2
  65. Segment(S1_1, S) → i_2
  66. Segment(B, S) → j_2
  67. Segment(C_1, S) → l_2
  68. Mirror(S, k) → S'
  69. Mirror(C_1, k) → D_1
  70. Mirror(S1_1, k) → E_1
  71. Arc(Mirror[Circle[S, C_1], k], D_1, E_1) → p_2
  72. Mirror(C_1, k) → F_1
  73. Mirror(S, k) → S'_1
  74. Segment(F_1, S'_1) → m_2
  75. Mirror(S1_1, k) → G_1
  76. Mirror(S, k) → S'_2
  77. Segment(G_1, S'_2) → n_2
  78. Mirror(B, k) → B'_1
  79. Mirror(S, k) → S'_3
  80. Segment(B'_1, S'_3) → q_2
  81. Segment(V', E_1) → r_2
  82. Mirror(V', k) → V''
  83. Mirror(E_1, k) → H_1
  84. Segment(V'', H_1) → s_2
  85. Segment(V, S) → h
  86. Mirror(V, k) → V'_2
  87. Mirror(S, k) → S'_4
  88. Segment(V'_2, S'_4) → h'

AI Drawing Prompt Reference

Create a Tudor arch architectural element. Start by defining two base points for the arch endpoints and connect them to form the doorway segment. Find the midpoint of the doorway and draw a perpendicular line upward from it. Draw two circles—one centered at the midpoint through the top point, and another centered at the top point through the midpoint—their intersection determines the arch control point. Connect the midpoint with the control point to form the arc support line. Create circular arcs using the endpoints and control point to form the arch edges. Mirror the entire arch structure horizontally to complete the Tudor arch. Add decorative polygonal elements below the arch to finish the design.
The prompt above was compiled from the original drawing commands and is for reference only.