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Google Chrome Logo Geometric Construction

Google Chrome Logo Geometric Construction
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2019-09-22 05:04
CircleFunctionTrigonometry
This example demonstrates how to construct the Google Chrome Logo geometrically using GeoGebra. It involves core mathematical concepts such as area, circle, geometry, plane figures, rotation, trigonometric functions, equations, unit circle, exponential functions, and random experiments. The construction utilizes commands and objects like Polygon, Midpoint, Vector, OrthogonalVector, Line, OrthogonalLine, Circle, Intersect, Segment, Rotate, CircleArc, Mirror, Semicircle, and CircleSector. It is suitable for high school students learning complex geometric constructions and for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Midpoint(D, A) → E
  3. Midpoint(D, B) → G
  4. Vector(A, B) → u
  5. OrthogonalVector(u) → v
  6. Line(A, B) → m
  7. OrthogonalLine(G, m) → n
  8. Line(E, G) → j
  9. Circle(G, E) → c
  10. Circle(G, F) → d
  11. Circle(G, H) → e
  12. Intersect(e, n) → I, J
  13. OrthogonalLine(J, n) → k
  14. Intersect(c, k) → K, L
  15. Segment(J, K) → l
  16. Rotate(J, 120°, G) → J'
  17. Rotate(K, 120°, G) → K'
  18. Segment(J', K') → l'
  19. Rotate(J', 120°, G) → J''
  20. Rotate(K', 120°, G) → K''
  21. Segment(J'', K'') → l''
  22. CircleArc(G, K, K') → p
  23. Intersect(k, l') → M
  24. Polygon(K, K', J', J) → q1, k_1, k', j', j_1
  25. Rotate(p, 120°, G) → p'
  26. Rotate(K, 120°, G) → K'_1
  27. Rotate(K', 120°, G) → K''_1
  28. Rotate(J', 120°, G) → J''_1
  29. Rotate(J, 120°, G) → J'_1
  30. Polygon(K'_1, K''_1, J''_1, J'_1) → q1', k'_1, k''_1, j''_1, j'_1
  31. Rotate(p', 120°, G) → p''
  32. Rotate(K'_1, 120°, G) → N
  33. Rotate(K''_1, 120°, G) → O
  34. Rotate(J''_1, 120°, G) → P
  35. Rotate(J'_1, 120°, G) → Q
  36. Polygon(N, O, P, Q) → q1'', n_1, o_1, p_1, q
  37. Mirror(J, G) → J'_2
  38. Polygon(J'', J'_2, K'') → t1, k'', j'', j'_2
  39. Rotate(J'', 120°, G) → J'''
  40. Rotate(J'_2, 120°, G) → R
  41. Rotate(K'', 120°, G) → K'''
  42. Polygon(J''', R, K''') → t1', k''', j''', r
  43. Rotate(J''', 120°, G) → S
  44. Rotate(R, 120°, G) → R'
  45. Rotate(K''', 120°, G) → T
  46. Polygon(S, R', T) → t1'', t, s, r'
  47. Mirror(F, G) → F'
  48. Semicircle(F, F') → c_1
  49. Rotate(F', (-(20°)), G) → F''
  50. CircleSector(G, F'', F') → d_1
  51. Mirror(d_1, n) → e_1