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Geometric Construction of the TripAdvisor Owl Logo

Geometric Construction of the TripAdvisor Owl Logo
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2019-05-31 23:50
CircleAngleVectorTransformationGeometric Construction
① This GeoGebra example reconstructs the outline of the TripAdvisor owl logo, demonstrating how circles, line segments, polygons, and rotations can be combined to form a complex graphic. ② Core mathematical concepts include circle intersections, orthogonal lines, vector reflection, rotational symmetry, angle measurement, and polygon filling, all within two-dimensional vector geometry. ③ Construction highlights: from the summary, commands such as Line, OrthogonalLine, Circle, Intersect, Vector, Mirror, OrthogonalVector, CircleSector, Rotate, Angle, and Polygon are used, along with numerous auxiliary points (A, B, C, D, E, F, G, H, I, J, K, L, M) and objects (texto1, imagen1, circle c, segments d, e, k, p, r, etc.). Symmetric parts are generated via rotation and mirroring to complete the logo. ④ Suitable for middle or high school geometry classes, or as a mathematical modeling exercise in graphic design, helping students understand geometric transformations (rotation, reflection) and the integrated use of basic construction tools.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. OrthogonalLine(B, f) → g
  3. OrthogonalLine(A, f) → h
  4. Circle(A, B) → c
  5. Intersect(c, h) → C, D
  6. OrthogonalLine(D, g) → i
  7. OrthogonalLine(C, g) → j
  8. Vector(A, B) → u
  9. Circle(A, H) → d
  10. Circle(A, G) → e
  11. Circle(A, F) → k
  12. Circle(A, E) → p
  13. Mirror(D, g) → D'
  14. OrthogonalVector(u) → v
  15. CircleSector(I, D', D) → q
  16. Mirror(J, g) → J'
  17. CircleSector(I, J', J) → r
  18. Intersect(g, i) → K
  19. Mirror(K, h) → K'
  20. Rotate(J, (-(68°)), K') → J'_1
  21. Angle(J'_1, K', J) → α
  22. Line(K', J'_1) → l
  23. Intersect(c, l) → L, M
  24. Polygon(D, K', L) → t1, l_1, d_1, k'
  25. Intersect(j, g) → N
  26. Line(F, N) → m
  27. Intersect(c, m) → O, P
  28. Polygon(N, B, P) → t2, p_1, n, b
  29. Line(I, A) → s
  30. Intersect(c, s) → Q, R
  31. Polygon(N, P, Q, I) → q1, n_1, p_2, q_1, i_1
  32. Mirror(p, g) → p'
  33. Mirror(k, g) → k'_1
  34. Mirror(e, g) → e'
  35. Mirror(d, g) → d'
  36. Mirror(c, g) → c'
  37. Mirror(k, g) → k'_2
  38. Mirror(p, g) → p'_1
  39. Mirror(D, g) → D'_1
  40. Mirror(K', g) → K''
  41. Mirror(L, g) → L'
  42. Polygon(D'_1, K'', L') → t1', l', d'_1, k''
  43. Mirror(N, g) → N'
  44. Mirror(P, g) → P'
  45. Mirror(Q, g) → Q'
  46. Mirror(I, g) → I'
  47. Polygon(N', P', Q', I') → q1', n', t, q', i'
  48. Mirror(N, g) → N'_1
  49. Mirror(B, g) → B'
  50. Mirror(P, g) → P'_1
  51. Polygon(N'_1, B', P'_1) → t2', a, n'_1, b'