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19. Seurat's Circus

19. Seurat's Circus
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2023-03-20 19:56
CircleParametric EquationGeometric Construction
In collections geometriadinamica.es
This example demonstrates the magic of a circle, showcasing the area and circumference of a circle. Key mathematical concepts include the area and circumference of a circle, as well as geometric transformations. The construction involves using GeoGebra commands such as OrthogonalLine, Point, Segment, If, Dilate, Circle, Intersect, Polygon, Line, CircleArc, Midpoint, and objects A_1, B, a, C, b, M_1, pas, t_1, B_1, A, d, A_3, P_0, P_8, esc, P_1, P_2, P_3, P_4, P_5, P_6, P_7, t_2, t_3, t_4, t_5, t_6, A_2, A_4, A_5, A_6, B_2, B_3, B_4, B_5, B_6, D, pr, e, E. Suitable for middle school math, calculating the area and circumference of a circle, and applying geometric transformations.

GeoGebra Commands & Parameters

  1. OrthogonalLine(B, xAxis) → a
  2. Point(a) → C
  3. Segment(B, C) → b
  4. Point(b) → M_1
  5. If(pas > 0 ∧ pas < 7, 0, -1) → t_1
  6. OrthogonalLine(A, b) → d
  7. If(pas > 1 ∧ pas < 7, 0, -1) → t_2
  8. If(pas > 2 ∧ pas < 7, 0, -1) → t_3
  9. If(pas > 3 ∧ pas < 7, 0, -1) → t_4
  10. If(pas > 4 ∧ pas < 7, 0, -1) → t_5
  11. If(pas > 5 ∧ pas < 7, 0, -1) → t_6
  12. Point(d) → D
  13. OrthogonalLine(A, b) → e
  14. Dilate(D, pr, A) → E
  15. Circle(A, E) → f
  16. OrthogonalLine(A, e) → g
  17. Intersect(f, g, 2) → F
  18. OrthogonalLine(F, g) → h
  19. OrthogonalLine(D, e) → i
  20. Intersect(h, i) → G
  21. Segment(P_1, P_7) → c
  22. Polygon(A, F, G, D) → P, a_1, f_1, g_1, d_1
  23. Circle(A, F) → k
  24. Circle(D, G) → p
  25. Dilate(D, fi, A) → L
  26. Circle(A, L) → t
  27. Intersect(t, a_1) → H,
  28. OrthogonalLine(H, a_1) → j
  29. Intersect(j, g_1) → I
  30. Circle(D, I) → q
  31. Segment(A, B_1) → l
  32. Intersect(q, l) → J,
  33. Intersect(t, l) → K,
  34. Line(K, b) → m
  35. Line(J, b) → n
  36. Intersect(n, j) → M
  37. Intersect(m, j) → N
  38. Segment(H, I) → r
  39. CircleArc(A, K, H) → s
  40. CircleArc(D, I, J) → c_1
  41. Segment(M, J) → b_1
  42. Segment(N, K) → e_1
  43. Circle(H, M) → p_1
  44. Circle(A, J) → q_1
  45. Segment(F, B_2) → i_1
  46. Intersect(q_1, i_1) → O,
  47. Intersect(p_1, i_1) → Q,
  48. OrthogonalLine(Q, b) → j_1
  49. OrthogonalLine(O, b) → l_1
  50. Intersect(l_1, b_1) → R
  51. Intersect(e_1, l_1) → S
  52. Segment(O, R) → m_1
  53. Intersect(l_1, g_1) → T
  54. Intersect(j_1, g_1) → U
  55. Intersect(j_1, e_1) → V
  56. Segment(O, R) → h_1
  57. Intersect(j_1, b_1) → W
  58. Segment(Q, W) → k_1
  59. Segment(S, T) → n_1
  60. OrthogonalLine(B_3, b) → r_1
  61. Intersect(r_1, i_1) → Y
  62. Intersect(r_1, g_1) → Z
  63. Intersect(g_1, r_1) → C_1
  64. Segment(C_1, A) → s_1
  65. Point(c_1) → D_1
  66. Segment(C_1, J) → a_2
  67. Segment(C_1, K) → b_2
  68. Segment(Y, J) → c_2
  69. Segment(Y, K) → d_2
  70. Segment(Y, D) → e_2
  71. Segment(D, B_4) → f_2
  72. Intersect(g_1, f_2) → E_1
  73. Intersect(f_2, i_1) → F_1
  74. Segment(F_1, M) → g_2
  75. Segment(F_1, N) → h_2
  76. Segment(E_1, N) → i_2
  77. Segment(E_1, M) → j_2
  78. OrthogonalLine(B_5, b) → k_2
  79. Intersect(b_1, k_2) → G_1
  80. Intersect(e_1, k_2) → I_1
  81. Segment(V, O_1) → c_3
  82. CircleArc(A, J, O) → d_3
  83. CircleArc(D, T, L) → e_3
  84. Point(k_2) → J_1
  85. Point(k_2) → Q_1
  86. Point(k_2) → R_1
  87. Midpoint(H, I) → U_1
  88. OrthogonalLine(U_1, r) → l_2
  89. Segment(R_1, U_1) → m_2
  90. Segment(U_1, J_1) → n_2
  91. Segment(Q_1, M) → p_2
  92. Segment(Q_1, N) → q_2
  93. OrthogonalLine(B_6, b) → r_2
  94. Point(r_2) → H_1
  95. Point(r_2) → K_1
  96. Point(r_2) → L_1
  97. Segment(L_1, R_1) → s_2
  98. Segment(K_1, Q_1) → a_3
  99. Segment(J_1, H_1) → b_3

AI Drawing Prompt Reference

Draw a geometric composition based on a horizontal baseline. Start with a vertical auxiliary line, pick a point on it, and connect it to a fixed point on the baseline to form a segment, marking its midpoint. From another fixed point, draw a perpendicular to this segment, choose a point on it, and use a dilation to get a point on a circle, then draw that circle centered at the first fixed point. Find intersections with another perpendicular, construct a rectangle, and inside it, draw multiple circles and arcs with different centers and radii, connecting relevant intersection points to create a symmetric decorative pattern. The final figure includes circles, arcs, segments, and a rectangle, evoking a circus-like geometric aesthetic.
The prompt above was compiled from the original drawing commands and is for reference only.