Shell Logo

Shell Logo
Loading the math board and drawing, please wait…
2019-05-22 04:42
This GeoGebra example demonstrates the geometric construction of the Shell logo. Key mathematical concepts include vectors, rotation, circles, and angles. Using commands like LineBisector, Midpoint, Vector, and Rotate, the essential elements of the logo are constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → f
  2. Midpoint(A, B) → C
  3. Vector(A, C) → u
  4. OrthogonalVector(u) → v
  5. Rotate(A, (-(120°)), E) → A'_1
  6. Vector(E, A'_1) → w
  7. Rotate(H, 45°, F) → H'_2
  8. Line(F, H'_2) → m
  9. Mirror(H, f) → H'
  10. OrthogonalLine(F, f) → j
  11. Line(I, j) → k
  12. Intersect(f, k) → M
  13. Intersect(f, j) → G
  14. Vector(M, G) → c
  15. CircleArc(N, H', H) → e
  16. Intersect(e, m) → Q, R
  17. Mirror(D, f) → D'
  18. Segment(A, D') → g
  19. Segment(A, E) → h
  20. Segment(F, E) → i
  21. Vector(F, H) → a
  22. OrthogonalVector(a) → b
  23. Mirror(F, f) → F'
  24. CircleArc(N, F', F) → d
  25. Rotate(Q, (-(23.5°)), N) → H'_1
  26. Rotate(H'_1, (-(23.5°)), N) → P
  27. Rotate(P, (-(23.5°)), N) → P'
  28. Angle(A'_1, E, A) → γ
  29. Angle(H, F, H'_2) → α
  30. Line(E, m) → l
  31. Line(Q, i) → n
  32. Line(N, j) → q
  33. Rotate(P', (-(23.5°)), N) → P''
  34. Rotate(H'_1, (-(5°)), N) → T
  35. Rotate(P, (-(5°)), N) → P'_1
  36. Rotate(P', (-(5°)), N) → P''_1
  37. Line(I, f) → r
  38. Intersect(n, r) → J
  39. Intersect(r, g) → K
  40. Polygon(F, Q, J, O, L, D', A, E) → polígono1, f_1, q_1, j_1, o_1, l_1, d', a_1, e_1
  41. Mirror(P'', f) → P'''
  42. Mirror(F, f) → F'_1
  43. Mirror(Q, f) → Q'_1
  44. Mirror(J, f) → J'
  45. Mirror(O, f) → O'
  46. Mirror(L, f) → L'
  47. Mirror(D', f) → D''
  48. Mirror(A, f) → A'
  49. Mirror(E, f) → E'
  50. Polygon(F'_1, Q'_1, J', O', L', D'', A', E') → polígono1', f'_1, q'_1, j', o', l', d'', a', e'
  51. Polygon(P'', P''', G) → t1, g_1, p'', p'''
  52. Intersect(f, n) → U
  53. CircleArc(S, J', J) → p
  54. Rotate(J, (-(6°)), S) → J'_1
  55. Rotate(J'_1, (-(6°)), S) → V
  56. Rotate(V, (-(6°)), S) → V'
  57. Polygon(H'_1, T, J'_1) → t2, j'_1, h'_1, t
  58. Polygon(P, P'_1, V) → t3, v_1, p_1, p'_1
  59. Polygon(P', P''_1, V') → t4, v', p', p''_1
  60. Mirror(P', f) → P''_2
  61. Mirror(P''_1, f) → W
  62. Mirror(V', f) → V''
  63. Polygon(P''_2, W, V'') → t4', v'', p''_2, w_1
  64. Mirror(P, f) → P'_2
  65. Mirror(P'_1, f) → Z
  66. Mirror(V, f) → V'_1
  67. Polygon(P'_2, Z, V'_1) → t3', v'_1, p'_2, z_1
  68. Mirror(H'_1, f) → A_1
  69. Mirror(T, f) → T'
  70. Mirror(J'_1, f) → B_1
  71. Polygon(A_1, T', B_1) → t2', b_1, s, t'
  72. CircleArc(C_1, L, L') → c_1
  73. CircleArc(D_1, D', D) → d_1
  74. Polygon(L, L', D, D') → c1, l_2, h_1, d_2, i_1
  75. Mirror(H'_1, f) → E_1
  76. Intersect(j, n) → F_1
  77. Mirror(F_1, f) → G_1
  78. Polygon(F_1, J, O, O', J', G_1) → polígono2, k_1, j_2, o_2, m_1, n_1, r_1
  79. Segment(L, L') → s_1

AI Drawing Prompt Reference

Draw the Shell logo by first constructing the perpendicular bisector f of line segment AB, then finding the midpoint C, creating vector u from A to C, and its orthogonal vector v. Rotate point A 120 degrees around point E to get A'_1, and rotate point H 45 degrees around point F to get H'_2. Continue with these steps to build the various components of the logo, ultimately forming a complete Shell logo.
The prompt above was compiled from the original drawing commands and is for reference only.