MathPlotAI Logo MathPlotAI

Geometric Construction of the Paris Chamber of Commerce Logo

Geometric Construction of the Paris Chamber of Commerce Logo
Loading the math board and drawing, please wait…
2019-12-14 01:30
TriangleCirclePolygonTransformationGeometric Construction
① This GeoGebra example precisely reconstructs the logo of the Paris Chamber of Commerce and Industry (CCI Paris), demonstrating how to build a symmetric emblem using fundamental geometric elements. ② Core mathematical concepts include equilateral triangles, circles, symmetry, rotation, vectors, perpendicular lines, angle bisectors, polygons, and circular sectors, covering classic two-dimensional geometry constructions and transformations. ③ Construction highlights: from the summary, the commands used are Line, OrthogonalLine, LineBisector, Vector, OrthogonalVector, Mirror, Intersect, Circle, Rotate, Midpoint, Polygon, CircleSector, and Segment, with objects such as A, B, s, b, m, u, v, I, h, C, d, N, O, K, P, F, E, q, j, N_1, l, f, U, J, G, M, i, S, Q, H, g, D, M', etc., built step by step and combined via symmetry transformations to form the complete logo. ④ Suitable for high school or university geometry courses, mathematical modeling, or design education, to illustrate geometric construction, symmetry transformations, and the mathematical principles behind graphic design, as well as a comprehensive practice case for advanced 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. LineBisector(A, C) → d
  8. Mirror(h, d) → h'
  9. Intersect(m, h') → N
  10. Intersect(m, d) → E
  11. Circle(E, P) → q
  12. Line(F, E) → j
  13. Rotate(j, (7 * π / 18), E) → j'_1
  14. Line(N_1, j) → l
  15. OrthogonalLine(C, v, xOyPlane) → f
  16. Intersect(f, m) → U
  17. Midpoint(C, A) → J
  18. OrthogonalLine(M, d) → i
  19. Mirror(i, m) → i'
  20. Intersect(h, m) → S
  21. Mirror(Q, m) → Q'
  22. OrthogonalLine(B, u, xOyPlane) → g
  23. Intersect(g, f) → D
  24. Mirror(M, m) → M'
  25. Midpoint(E, M') → L
  26. Intersect(g, h') → A_1
  27. Polygon(A, B, D, C) → q11, a_3, b_2, d_2, c_3
  28. Circle(E, N) → c
  29. Circle(E, O) → k
  30. Circle(E, K) → p
  31. Intersect(c, j) → R, T
  32. Intersect(k, j) → V, W
  33. Intersect(p, j) → Z, B_1
  34. Intersect(q, j) → C_1, E_1
  35. Intersect(c, j'_1) → F_1, G_1
  36. Intersect(k, j'_1) → H_1, I_1
  37. Intersect(p, j'_1) → J_1, K_1
  38. Intersect(q, j'_1) → L_1, M_1
  39. Circle(E, O_1) → e_1
  40. Circle(E, P_1) → f_1
  41. CircleSector(E, R, G_1) → r
  42. CircleSector(E, C_1, M_1) → d_1
  43. CircleSector(E, V, I_1) → t
  44. CircleSector(E, Z, K_1) → c_1
  45. Rotate(l, (7 * π / 18), E) → j'
  46. Intersect(e_1, j') → Q_1, R_1
  47. Intersect(f_1, j') → S_1, T_1
  48. Intersect(c, l) → U_1, V_1
  49. Intersect(f_1, l) → W_1, Z_1
  50. Rotate(U_1, (-(35°)), W_1) → A_2
  51. CircleSector(W_1, A_2, U_1) → e
  52. Rotate(W_1, (-(15°)), E) → B_2
  53. Line(A_2, W_1) → n
  54. Line(B_2, n) → a
  55. Intersect(e_1, a) → C_2, G_2
  56. Intersect(a, j') → H_2
  57. CircleSector(E, R_1, C_2) → g_1
  58. CircleSector(E, T_1, B_2) → h_1
  59. Polygon(E, R_1, H_2) → t1, i_1, j_1, l_1
  60. CircleSector(E, Z, K_1) → k_1
  61. Segment(E, R) → m_1
  62. Segment(E, I_1) → n_1
  63. Segment(E, C_2) → p_1
  64. Segment(E, R_1) → q_1

AI Drawing Prompt Reference

Draw the Paris Chamber of Commerce logo by first creating line segment AB, then constructing its perpendicular and angle bisector lines, using vectors and rotations to generate key points and segments, and finally forming the overall shape through mirroring and intersection operations.
The prompt above was compiled from the original drawing commands and is for reference only.