MathPlotAI Logo MathPlotAI

Geometric Construction of the Caixa Geral de Depósitos Logo

Geometric Construction of the Caixa Geral de Depósitos Logo
Loading the math board and drawing, please wait…
2019-12-13 03:26
PolygonAngleVectorTransformationGeometric Construction
This GeoGebra example demonstrates how to construct the logo of Caixa Geral de Depósitos (a Portuguese bank) using precise geometric construction tools. The core mathematical concepts involved include lines, perpendiculars, angle bisectors, vectors, reflection symmetry, midpoints, and polygons. The construction process utilizes commands such as Line, OrthogonalLine, LineBisector, Vector, OrthogonalVector, Intersect, Mirror, Midpoint, and Polygon to create the necessary auxiliary lines, define directions, find intersection points, apply symmetry, and assemble the final shape. This example is suitable for middle or high school geometry classes, as well as math clubs, to illustrate the logic of geometric construction and the practical use of GeoGebra commands.

GeoGebra Commands & Parameters

  1. Line(A, B) → s
  2. OrthogonalLine(A, s) → b
  3. LineBisector(A, B) → m
  4. Vector(A, B) → u
  5. OrthogonalVector(u) → v
  6. OrthogonalLine(I, b) → h
  7. OrthogonalLine(C, v, xOyPlane) → f
  8. Intersect(f, m) → U
  9. LineBisector(A, C) → d
  10. Mirror(h, d) → h'
  11. Intersect(m, h') → N
  12. Midpoint(C, A) → J
  13. Line(G, d) → j
  14. Mirror(j, d) → j'
  15. OrthogonalLine(M, d) → i
  16. Mirror(i, m) → i'
  17. Intersect(i', j') → K
  18. Mirror(K, m) → K'
  19. Intersect(m, d) → E
  20. Line(O, j) → l
  21. Mirror(l, d) → l'
  22. Line(F, K) → k
  23. Line(P, k) → n
  24. Intersect(d, n) → L_1
  25. Mirror(n, m) → n'
  26. Line(T, n') → q
  27. Intersect(q, l') → E_1
  28. Intersect(j', n') → N_1
  29. Intersect(k, j) → R
  30. Line(R, n') → p
  31. Mirror(p, m) → p'
  32. Line(K', p') → r
  33. Intersect(r, h) → F_1
  34. Mirror(r, m) → r'
  35. Line(P, r') → t
  36. Mirror(t, m) → t'
  37. Intersect(l', t') → O_1
  38. Intersect(d, p') → M_1
  39. Mirror(k, m) → k'
  40. Intersect(k', j) → W
  41. Intersect(h, m) → S
  42. Mirror(q, m) → q'
  43. Intersect(q', m) → C_1
  44. Intersect(d, q') → I_1
  45. Intersect(l', p) → J_1
  46. Mirror(F_1, m) → G_1
  47. Intersect(t, l') → K_1
  48. Mirror(F, m) → F'
  49. Intersect(l, n') → Z
  50. Intersect(j, n) → V
  51. Intersect(l, n) → B_1
  52. Mirror(Q, m) → Q'
  53. OrthogonalLine(B, u, xOyPlane) → g
  54. Intersect(g, f) → D
  55. Mirror(M, m) → M'
  56. Midpoint(E, M') → L
  57. Intersect(g, h') → A_1
  58. OrthogonalLine(D_1, m) → e
  59. Polygon(A, B, D, C) → q11, a_3, b_2, d_2, c_3
  60. Mirror(V, m) → V'
  61. Polygon(A_2, Z_1, K', F_1, S, C_2, B_2, E_1, O_1, N_1) → poly3, c_1, n_2, d_1, e_1, f_2, g_2, h_2, k_2, l_2, m_2
  62. Polygon(F, F', W, S_1, R_1, H_1, Z, B_1, Q_1, P_1) → poly1, a, m_1, c, f_1, g_1, h_1, i_1, j_1, k_1, l_1
  63. Polygon(T_1, R, K, G_1, W_1, V_1, K_1, P, L_1, U_1) → poly2, n_1, j_2, p_1, q_1, r_1, s_1, t_1, a_1, b_1, i_2

AI Drawing Prompt Reference

Draw a geometric logo using lines, perpendiculars, angle bisectors, vectors, and reflection symmetry to create multiple polygons. Start with a base line, then construct its perpendicular and angle bisector. Use vectors and orthogonal vectors to define directions, and apply intersection and reflection to form symmetric structures. Finally, assemble the final shape using these auxiliary lines to demonstrate geometric construction logic and symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.