Ghirlandaio's Adoration

Ghirlandaio's Adoration
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2023-03-20 19:45
In collections geometriadinamica.es
This example demonstrates some mathematical concepts in Ghirlandaio's Adoration scene. It involves geometric shapes' symmetry, similar triangles, and complex numbers. Through GeoGebra's construction, users can see the relationships and symmetries between different elements in the Adoration scene. This example is suitable for middle school or high school students learning geometric shapes' symmetry and similar triangles.

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 > 5 ∧ pas < 7, 0, -1) → t_6
  6. If(pas > 4 ∧ pas < 7, 0, 1000000) → t_5
  7. OrthogonalLine(B_5, b) → s_1
  8. If(pas > 3 ∧ pas < 7, 0, 1000000) → t_4
  9. Line(B_4, b) → r_1
  10. If(pas > 0 ∧ pas < 7, 0, 1000000) → t_1
  11. OrthogonalLine(B_1, b) → m
  12. OrthogonalLine(A, b) → d
  13. If(pas > 1 ∧ pas < 7, 0, 1000000) → t_2
  14. If(pas > 2 ∧ pas < 7, 0, 1000000) → t_3
  15. Point(d) → D
  16. OrthogonalLine(A, b) → e
  17. Dilate(D, pr, A) → E
  18. Circle(A, E) → f
  19. OrthogonalLine(A, e) → g
  20. Intersect(f, g, 2) → F
  21. OrthogonalLine(F, g) → h
  22. OrthogonalLine(D, e) → i
  23. Intersect(h, i) → G
  24. Segment(P_1, P_7) → c
  25. Polygon(A, F, G, D) → P, a_1, f_1, g_1, d_1
  26. Midpoint(F, D) → H
  27. Point(m) → I
  28. Rotate(I, 90°, H) → J
  29. Mirror(I, H) → K
  30. Mirror(J, H) → L
  31. Rotate(I, 45°, H) → M
  32. OrthogonalLine(B_2, b) → k
  33. Point(k) → O
  34. Rotate(O, 90°, H) → Q
  35. Mirror(O, H) → R
  36. Mirror(Q, H) → S
  37. Polygon(I, J, K, L) → T, i_1, j, k_1, l
  38. Polygon(O, Q, R, S) → U, o, q, r, s
  39. Line(B_3, b) → n
  40. Point(n) → V
  41. Point(n) → W
  42. OrthogonalLine(V, n) → p
  43. OrthogonalLine(W, n) → t
  44. Point(p) → Y
  45. Point(t) → Z
  46. Polygon(V, Y, Z, W) → Q_1, v, y, z, w
  47. Point(n) → C_1
  48. Point(n) → D_1
  49. OrthogonalLine(D_1, n) → b_1
  50. OrthogonalLine(C_1, n) → c_1
  51. Point(b_1) → E_1
  52. Point(b_1) → G_1
  53. Point(c_1) → H_1
  54. Point(c_1) → I_1
  55. Polygon(E_1, H_1, I_1, G_1) → R_1, e_1, h_1, i_2, g_2
  56. Line(B_4, b) → j_1
  57. Point(r_1) → F_1
  58. Point(j_1) → K_1
  59. OrthogonalLine(K_1, j_1) → l_1
  60. Point(s_1) → O_1
  61. Segment(W, O_1) → m_1
  62. Point(s_1) → N_1
  63. Segment(N_1, Z) → n_1
  64. Point(r_1) → J_1
  65. Segment(I_1, J_1) → p_1
  66. Segment(G_1, F_1) → q_1
  67. Line(A_6, b) → a_2
  68. Point(p_1) → L_1
  69. Line(B_6, b) → b_2
  70. Point(b_2) → S_1
  71. Circle(S_1, L_1) → c_2
  72. OrthogonalLine(M_1, b) → d_2
  73. Intersect(d_2, c) → T_1

AI Drawing Prompt Reference

This is a geometric figure based on symmetry and similar triangles, containing circles, line segments, and polygons. Construct these using coordinate geometry and apply transformations like rotation and reflection to highlight symmetry. The figure consists of points, line segments, and circles, forming a complex geometric structure suitable for learning symmetry and similar triangles.
The prompt above was compiled from the original drawing commands and is for reference only.