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Leonardo's Last Supper Geometric Construction

Leonardo's Last Supper Geometric Construction
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2023-03-20 19:52
CirclePolygonCoordinate GeometryTransformationGeometric Construction
In collections geometriadinamica.es
This example dynamically demonstrates geometric constructions inspired by Leonardo da Vinci's 'The Last Supper', focusing on composition and symmetry. It involves core math concepts like geometric construction, coordinate geometry, similarity transformations, and fractal geometry. GeoGebra commands and objects used include Line, OrthogonalLine, Point, Dilate, Circle, Intersect, Polygon, Midpoint, Segment, and CircleArc. Suitable for high school students and enthusiasts in mathematical art and geometric constructions.

GeoGebra Commands & Parameters

  1. Line(H1, H2) → a
  2. OrthogonalLine(A, a) → c
  3. Line(A, a) → b
  4. Point(b) → B
  5. OrthogonalLine(B, b) → f
  6. Dilate(B, pr, A) → Dil
  7. Circle(A, Dil) → d
  8. Intersect(d, c) → D5, C
  9. OrthogonalLine(C, c) → e
  10. Intersect(f, e) → D
  11. If(paso > 0 ∧ paso < 7, 1, 0) → t_1
  12. If(paso > 1 ∧ paso < 7, 1, 0) → t_2
  13. If(paso > 2 ∧ paso < 7, 1, 0) → t_3
  14. If(paso > 3 ∧ paso < 7, 1, 0) → t_4
  15. If(paso > 4 ∧ paso < 7, 1, 0) → t_5
  16. If(paso > 5 ∧ paso < 7, 1, 0) → t_6
  17. Polygon(A, B, D, C) → P, a_1, b_1, d_1, c_1
  18. Point(b_1) → W_2
  19. Midpoint(A, B) → F
  20. Circle(A, F) → g
  21. Circle(B, F) → h
  22. Intersect(g, c_1) → E,
  23. Intersect(h, b_1) → G,
  24. Segment(E, G) → i
  25. OrthogonalLine(B_1, a_1) → j
  26. Point(j) → H
  27. CircleArc(A, H, E) → k
  28. CircleArc(B, G, H) → p
  29. Intersect(j, i) → I
  30. Segment(H, I) → l
  31. OrthogonalLine(B_2, a_1) → m
  32. Point(m) → K
  33. Midpoint(A, K) → L
  34. Midpoint(K, B) → M
  35. OrthogonalLine(M, a_1) → n
  36. OrthogonalLine(L, a_1) → q
  37. Intersect(i, q) → N
  38. Intersect(n, i) → O
  39. Segment(N, L) → r
  40. Segment(O, M) → s
  41. Segment(K, E) → f_1
  42. Segment(K, G) → g_1
  43. Intersect(m, i) → Q
  44. Segment(Q, A) → t
  45. Segment(Q, B) → e_1
  46. Circle(N, N1) → h_1
  47. Circle(N, N2) → k_1
  48. Circle(N, N4) → q_1
  49. Circle(N, N5) → r_1
  50. OrthogonalLine(B_3, a_1) → i_1
  51. Point(i_1) → S
  52. Point(i_1) → T
  53. Point(i_1) → U
  54. Point(i_1) → V
  55. Point(i_1) → W
  56. Point(i_1) → Y
  57. OrthogonalLine(G, i_1) → j_1
  58. Point(j_1) → Z
  59. Point(j_1) → C_1
  60. Point(j_1) → D_1
  61. Point(j_1) → E_1
  62. Point(j_1) → F_1
  63. Circle(O, F_1) → p_1
  64. Circle(O, E_1) → s_1
  65. Circle(O, D_1) → c_2
  66. Circle(O, C_1) → d_2
  67. Circle(O, Z) → e_2
  68. Circle(L, V) → f_2
  69. Circle(L, U) → g_2
  70. Circle(L, T) → h_2
  71. Circle(L, S) → k_2
  72. Circle(L, Y) → p_2
  73. Intersect(i_1, j_1) → H_1
  74. Circle(L, H_1) → q_2
  75. Intersect(g_2, a_1) → I_1, J_1
  76. Intersect(f_2, a_1) → K_1, L_1
  77. Intersect(h_2, a_1) → M_1,
  78. Intersect(k_2, a_1) → N_1,
  79. Intersect(p_2, a_1) → O_1,
  80. Intersect(q_2, a_1) → P_1,
  81. Intersect(p_1, s) → Q_1,
  82. Intersect(s_1, s) → R_1,
  83. Intersect(c_2, s) → S_1,
  84. Intersect(d_2, s) → T_1,
  85. Intersect(e_2, s) → U_1,
  86. Segment(Z, L_1) → l_1
  87. Segment(C_1, J_1) → m_1
  88. Segment(M_1, D_1) → n_1
  89. Segment(E_1, N_1) → a_2
  90. Segment(O_1, F_1) → b_2
  91. Segment(Q_1, Y) → i_2
  92. Segment(S, R_1) → j_2
  93. Segment(S_1, T) → l_2
  94. Segment(U, T_1) → m_2
  95. Segment(V, U_1) → n_2
  96. OrthogonalLine(B_4, a_1) → r_2
  97. Line(W_1, r_2) → s_2
  98. Line(Y_1, r_2) → a_3
  99. Line(Z_1, r_2) → b_3
  100. Point(s_2) → C_2
  101. Point(s_2) → D_2
  102. Point(r_2) → E_2
  103. Point(r_2) → F_2
  104. Point(a_3) → G_2
  105. Point(a_3) → H_2
  106. Point(b_3) → I_2
  107. Point(b_3) → J_2
  108. Polygon(C_2, I_2, J_2, D_2) → P_2, c_3, i_3, j_3, d_3
  109. Polygon(E_2, G_2, H_2, F_2) → Q_2, e_3, g_3, h_3, f_3
  110. Line(B_5, a_1) → k_3
  111. Point(k_3) → K_2
  112. Segment(K_2, E) → l_3
  113. Segment(K_2, N) → m_3
  114. Segment(K_2, N1) → n_3
  115. Segment(K_2, N2) → p_3
  116. Segment(K_2, D_1) → q_3
  117. Segment(K_2, N4) → r_3
  118. Segment(K_2, N5) → s_3
  119. Segment(K_2, O) → a_4
  120. Segment(K_2, G) → b_4
  121. Line(B_6, a_1) → c_4
  122. Point(c_4) → L_2
  123. Point(c_4) → M_2
  124. Point(c_4) → N_2
  125. Point(c_4) → O_2
  126. Circle(M_2, ra) → d_4
  127. Circle(L_2, ra) → e_4
  128. Circle(N_2, ra) → f_4
  129. Circle(O_2, ra) → g_4
  130. Midpoint(N, L) → R_2
  131. OrthogonalLine(R_2, c_1) → h_4
  132. Intersect(c_1, h_4) → S_2
  133. Intersect(b_1, h_4) → T_2
  134. Segment(S_2, T_2) → i_4
  135. Point(c_1) → U_2
  136. Segment(K_2, U_2) → j_4
  137. Segment(K_2, W_2) → k_4

AI Drawing Prompt Reference

Create a geometric composition inspired by Leonardo da Vinci's The Last Supper. Start with a horizontal baseline and a vanishing point above it. Draw radiating lines from the vanishing point to the two bottom corners of the canvas to establish perspective framework. Use the two bottom corners as endpoints to draw arcs intersecting at a point above, forming a trapezoidal figure layout area. Within the trapezoid, draw perpendicular and parallel lines to create a grid structure, then use key intersection points as centers to draw multiple concentric circles and circular arcs, creating radially symmetrical decorative patterns. The overall composition emphasizes the contrast between horizontal-vertical lines and curved arcs, reflecting the perspective principles and geometric beauty of Renaissance painting.
The prompt above was compiled from the original drawing commands and is for reference only.