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Vermeer's Allegory of Painting

Vermeer's Allegory of Painting
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2023-03-20 19:49
VectorTrigonometryCoordinate GeometryGeometric Construction
In collections geometriadinamica.es
This example demonstrates the geometric composition and perspective principles in Vermeer's painting 'Allegory of Painting'. It involves core mathematical concepts such as coordinate geometry, cosine theorem, statistical analysis, and the relationship between tangents and secants. The construction highlights GeoGebra commands and objects like Line, Point, Distance, OrthogonalLine, Intersect, Segment, and Midpoint. Suitable for high school and above learners to understand the integration of art and mathematics and geometric construction techniques.

GeoGebra Commands & Parameters

  1. Line(A, T) → a
  2. Point(a) → B
  3. Distance(A, B) → dx
  4. OrthogonalLine(A, a) → b
  5. Line(A, B) → c
  6. Line(A, C) → d
  7. OrthogonalLine(C, d) → e
  8. OrthogonalLine(B, c) → f
  9. Intersect(e, f) → D
  10. Distance(A, C) → dy
  11. Segment(Dφ1, Aφ1) → n
  12. Segment(Aφ2, Dφ2) → p
  13. Segment(Bφ2, Cφ2) → q
  14. Segment(Cφ1, Bφ1) → r
  15. Segment(C, Aφ1) → s
  16. Segment(C, Aφ2) → a1
  17. Segment(B, C) → b1
  18. Segment(Bφ1, C) → c1
  19. Segment(Bφ2, C) → d1
  20. Segment(D, Cφ2) → t
  21. Segment(D, Cφ1) → e1
  22. Segment(D, A) → f1
  23. Segment(D, Aφ1) → g1
  24. Segment(D, Aφ2) → h1
  25. Segment(A, Dφ1) → i1
  26. Segment(A, Dφ2) → j1
  27. Segment(A, Bφ2) → k1
  28. Segment(A, Bφ1) → l1
  29. Segment(B, Cφ1) → m1
  30. Segment(B, Cφ2) → n1
  31. Segment(B, Dφ1) → p1
  32. Segment(B, Dφ2) → q1
  33. Intersect(l1, m1) → E
  34. Intersect(k1, n1) → F
  35. Point(f) → G
  36. Intersect(d1, j1) → H
  37. Intersect(t, p1) → I
  38. Point(f) → J
  39. OrthogonalLine(J, f) → r1
  40. OrthogonalLine(I, f) → s1
  41. OrthogonalLine(F, f) → a2
  42. OrthogonalLine(E, f) → b2
  43. Intersect(n, b2) → K
  44. Intersect(f, b2) → L
  45. Intersect(p, a2) → M
  46. Intersect(n, s1) → O
  47. Intersect(f, s1) → P
  48. Segment(O, P) → d2
  49. Intersect(f, a2) → Q
  50. Intersect(s, a2) → R
  51. Segment(L, K) → e2
  52. Segment(Q, R) → f2
  53. Intersect(n, r1) → S
  54. Segment(J, S) → g2
  55. OrthogonalLine(G, f) → t1
  56. Intersect(j1, t1) → N
  57. Segment(N, G) → c2
  58. Midpoint(A, C) → U
  59. Midpoint(D, B) → V
  60. Midpoint(C, D) → W
  61. Midpoint(B, A) → Z
  62. Segment(U, D) → h2
  63. Segment(U, B) → i2
  64. Segment(V, A) → j2
  65. Segment(V, C) → k2
  66. Segment(W, A) → l2
  67. Segment(Z, C) → n2
  68. Segment(Z, D) → p2
  69. Segment(W, B) → m2

AI Drawing Prompt Reference

This drawing depicts the geometric composition in Vermeer's painting. It includes points, line segments, and intersection points. The construction order starts from basic points, drawing lines and perpendicular lines, then determining key positions through intersections. The drawing illustrates coordinate geometry and perspective principles, showing the integration of art and mathematics.
The prompt above was compiled from the original drawing commands and is for reference only.