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Google Logo Geometric Construction

Google Logo Geometric Construction
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2019-09-15 16:15
CirclePolygonVectorTransformationGeometric Construction
This example demonstrates the geometric construction of the Google Logo using GeoGebra. It involves core mathematical concepts such as vectors, circles, polygons, and geometric transformations. Key GeoGebra commands and objects used include Polygon, Midpoint, Vector, OrthogonalVector, Mirror, Line, OrthogonalLine, Intersect, Segment, Circle, CircleArc, and Semicircle. It is suitable for high school and above students to understand the application of geometric constructions and spatial transformations.

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. Mirror(F, E) → F'
  7. Line(F', C) → k
  8. Line(A, B) → m
  9. OrthogonalLine(G, m) → n
  10. Intersect(n, k) → H
  11. Line(F, B) → j
  12. Segment(I, K) → l
  13. Midpoint(H, I) → J
  14. Mirror(J, G) → J'
  15. Circle(G, L) → c
  16. OrthogonalLine(J, n) → p
  17. Mirror(p, G) → p'
  18. Circle(G, M) → d
  19. Intersect(c, p) → N, O
  20. Intersect(c, p') → P, Q
  21. Polygon(J, N, Q, J') → q1, j_1, n_1, q, j'
  22. CircleArc(G, Q, N) → e
  23. Intersect(d, j) → R, S
  24. Intersect(d, n) → T, U
  25. Semicircle(T, U) → r
  26. Polygon(J', M, T) → t1, t, s, m_1
  27. CircleArc(G, T, M) → c_1
  28. Intersect(c, j) → V, W
  29. Intersect(d, k) → Z, A_1
  30. Intersect(c, k) → B_1, C_1
  31. Polygon(S, M, Q, W) → q2, s_1, m_2, q_1, w
  32. CircleArc(G, W, Q) → d_1
  33. CircleArc(G, S, M) → e_1
  34. Segment(S, M) → a
  35. Polygon(Z, S, W, C_1) → q3, z_1, s_2, w_1, b
  36. CircleArc(G, C_1, W) → f_1
  37. CircleArc(G, Z, S) → g_1
  38. Segment(Z, S) → h_1
  39. Polygon(V, C_1, Z, R) → q4, v_1, i_1, z_2, r_1
  40. CircleArc(G, V, C_1) → k_1
  41. CircleArc(G, R, Z) → p_1
  42. Intersect(d, l) → D_1,
  43. Polygon(V, B_1, D_1, R) → q5, l_1, t_1, b_1, f_2
  44. CircleArc(G, D_1, R) → d_2
  45. Segment(R, D_1) → a_1
  46. CircleArc(G, B_1, V) → c_2
  47. Segment(V, B_1) → g_2