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ROBLOX Logo Geometric Construction

ROBLOX Logo Geometric Construction
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2020-06-13 23:13
CirclePolygonVectorTransformationGeometric Construction
This example demonstrates how to construct the ROBLOX Logo geometrically using GeoGebra. It involves core mathematical concepts such as 2D vectors, angles, squares, incircles, addition, normal distribution, real numbers, and multiplication. The construction utilizes commands like LineBisector, Line, OrthogonalLine, Vector, OrthogonalVector, Intersect, Mirror, Rotate, Polygon, CircleArc, and Sequence, along with objects like e_1, e_2, B, A, etc. It is suitable for high school mathematics education, showcasing vector operations, geometric transformations, and the construction of complex shapes.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → m
  2. Line(A, B) → s
  3. OrthogonalLine(A, s) → b
  4. Vector(A, B) → u
  5. OrthogonalVector(u) → v
  6. OrthogonalLine(F, b) → f
  7. OrthogonalLine(B_1, b) → a
  8. LineBisector(A_1, A) → l
  9. Intersect(m, l) → I
  10. Mirror(f, l) → f'
  11. OrthogonalLine(D, s) → i
  12. Intersect(i, f') → E
  13. OrthogonalLine(Z, i) → h
  14. OrthogonalLine(H, i) → k
  15. OrthogonalLine(N, h) → p
  16. Intersect(p, k) → O
  17. Rotate(O, (-(15°)), I) → O'_3
  18. Mirror(O, m) → O'
  19. Rotate(O', (-(15°)), I) → O''_2
  20. LineBisector(O'_3, O''_2) → n
  21. OrthogonalLine(G, b) → t
  22. OrthogonalLine(U, k) → q
  23. OrthogonalLine(A_1, b) → r
  24. OrthogonalLine(K, l) → j
  25. Intersect(t, j) → I_1
  26. OrthogonalLine(B, u, xOyPlane) → g
  27. Intersect(g, r) → C
  28. Mirror(f, l) → f'_1
  29. Mirror(F, l) → F'
  30. Polygon(A_1, C, B, A) → c4, a_1, c_3, b_2, a_2
  31. CircleArc(I_1, K, G) → c
  32. Intersect(m, f') → J
  33. Intersect(l, i) → L
  34. Intersect(m, k) → M
  35. Intersect(l, p) → P
  36. Intersect(h, q) → R
  37. Mirror(K, m) → K'
  38. Mirror(G, l) → G'
  39. Mirror(K, l) → K'_1
  40. Mirror(G, m) → G'_1
  41. Mirror(K'_1, m) → T
  42. Mirror(G', m) → G''
  43. Mirror(O, l) → O'_1
  44. Mirror(O', l) → O''
  45. Mirror(R, m) → R'
  46. Mirror(R', l) → R''
  47. Mirror(R, l) → R'_1
  48. Polygon(G'_1, K', K, G, G', K'_1, T, G'') → polígono1, g'_1, k', k_1, g_1, g', k'_1, t_1, g''
  49. Mirror(c, m) → c'
  50. Mirror(c, l) → c'_1
  51. Mirror(c'_1, m) → d
  52. Polygon(O', O'', O'_1, O) → c1, o', o'', o'_1, o
  53. Polygon(R, R', R'', R'_1) → c2, r_1, r', r'', r'_1
  54. Rotate(O', (-(30°)), I) → O''_1
  55. Rotate(O'', (-(30°)), I) → O'''
  56. Rotate(O'_1, (-(30°)), I) → Q
  57. Rotate(O, (-(30°)), I) → O'_2
  58. Rotate(O'', (-(15°)), I) → O'''_1
  59. Rotate(O'_1, (-(15°)), I) → S
  60. Polygon(O''_2, O'''_1, S, O'_3) → c1', o''_2, o'''_1, s_1, o'_3
  61. Rotate(R, (-(15°)), I) → R'_2
  62. Rotate(R', (-(15°)), I) → R''_1
  63. Rotate(R'', (-(15°)), I) → R'''
  64. Rotate(R'_1, (-(15°)), I) → V
  65. Polygon(R'_2, R''_1, R''', V) → c2', r'_2, r''_1, r''', v_1
  66. Intersect(n, a) → W
  67. Sequence(Polygon[Dilate[S, k, O''_2], Dilate[O'''_1, k, O''_2], Dilate[O''_2, k, O''_2], Dilate[O'_3, k, O''_2]], k, 0, 1, 0.03) → l1
  68. CircleArc(W, O'_3, O''_2) → e

AI Drawing Prompt Reference

Draw the ROBLOX logo by first constructing the perpendicular bisector of line segment AB, then drawing line AB and its perpendicular line b. Use vectors u and v to create a series of perpendicular and mirrored lines, and finally use rotations, reflections, and intersections to form the various parts of the complex geometric shape.
The prompt above was compiled from the original drawing commands and is for reference only.