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Mathematical Construction of F1 Logo

Mathematical Construction of F1 Logo
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2019-05-11 04:50
CirclePolygonVectorGeometric Construction
This example demonstrates how to mathematically construct the F1 logo. It involves core concepts like angles, circles, geometry, translation, vectors, and polygon construction. GeoGebra commands and objects used include Vector, Rotate, Line, Segment, Intersect, Angle, LineBisector, Midpoint, CircleArc, Distance, Polygon, Sequence, Point, and Translate. It is suitable for high school mathematics education, showcasing geometric transformations and the construction of complex shapes.

GeoGebra Commands & Parameters

  1. Vector(A, B) → v
  2. Rotate(B, (-(60°)), A) → B'
  3. Line(A, B') → h
  4. Vector(A, B') → u
  5. Line(D, h) → i
  6. Segment(A, B) → f
  7. Line(C, f) → g
  8. Line(B'_1, g) → n
  9. Line(M, n) → p
  10. Line(N, p) → q
  11. Line(P, q) → s
  12. Intersect(s, i) → R
  13. Angle(B', A, B) → α
  14. Line(E, i) → j
  15. Line(G, j) → k
  16. LineBisector(F, B'_1) → l
  17. Intersect(l, g) → J
  18. Line(A, B) → m
  19. Intersect(l, m) → K
  20. Midpoint(K, J) → L
  21. CircleArc(L, F, B'_1) → c
  22. Line(O, q) → r
  23. Midpoint(P, R) → Q
  24. Intersect(n, j) → H
  25. Intersect(n, i) → I
  26. Midpoint(P, R) → S
  27. Midpoint(R, S) → T
  28. Midpoint(P, S) → U
  29. Distance(D, G) → distanciaDG
  30. Intersect(r, i) → C_1
  31. Polygon(A, C, D, I, H, E, G, B) → polígono1, a, c_1, d, i_1, h_1, e, g_1, b
  32. Polygon(F, B'_1, G) → t1, g_2, f_1, b'_1
  33. Intersect(i, q) → D_1
  34. Intersect(k, p) → E_1
  35. Intersect(j, p) → F_1
  36. Polygon(N, P, R, D_1) → c1, n_1, p_1, r_1, d_1
  37. Polygon(U, P, V) → t2, v_1, u_1, p_2
  38. Polygon(U, W, S) → t4, s_1, u_2, w
  39. Polygon(T, S, Z) → t5, z_1, t_2, s_2
  40. Line(B_1, p) → t
  41. Intersect(p, i) → G_1
  42. Intersect(i, t) → H_1
  43. Sequence(H_1 + ((0.072 * β) * v), β, 1, 10) → l1
  44. Point(t) → J_1
  45. Translate(H_1, Vector[(0.075 * v)]) → K_1
  46. Translate(J_1, Vector[(0.075 * v)]) → M_1
  47. Translate(K_1, Vector[(0.075 * v)]) → N_1
  48. Translate(M_1, Vector[(0.075 * v)]) → P_1
  49. Translate(N_1, Vector[(0.075 * v)]) → Q_1
  50. Translate(P_1, Vector[(0.075 * v)]) → S_1
  51. Point(t) → U_1
  52. Polygon(A_1, R, T) → t3, t_1, a_1, r_2
  53. Point(t) → V_1
  54. Point(t) → L_1
  55. Polygon(H_1, I_1, L_1) → t6, l_1, j_1, k_1
  56. Sequence(Polygon[Translate[H_1, Vector[((0.072 * β) * v)]], Translate[I_1, Vector[((0.072 * β) * v)]], Translate[L_1, Vector[((0.072 * β) * v)]]], β, 1, 9) → l2
  57. Point(l1) → O_1
  58. Polygon(O_1, E_1, G_1, H_1) → c2, o_1, e_1, m_1, q_1

AI Drawing Prompt Reference

Draw a geometric construction of an F1 logo, involving angles, circles, geometric transformations, and vectors. Start by creating basic lines and vectors, then use rotations and reflections to form the various parts of the logo. Combine elements like line segments, midpoints, and arcs to create complex shapes, and finally assemble all parts into a complete logo.
The prompt above was compiled from the original drawing commands and is for reference only.