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LG Logo 2D Vector Geometry Construction

LG Logo 2D Vector Geometry Construction
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2019-07-01 04:50
CircleAngleVectorInequalityGeometric Construction
This example demonstrates the geometric construction of the LG logo using 2D vectors. It involves core mathematical concepts such as vectors, angles, area, circles, geometric constructions, inequalities, median lines, and geometric means. GeoGebra commands and objects used include LineBisector, Line, Intersect, Vector, OrthogonalVector, Mirror, OrthogonalLine, Midpoint, Rotate, Circle, CircleArc, Polygon, Semicircle, CircleSector, Segment, and CurveCartesian. Suitable for high school mathematics teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → g
  2. Line(A, B) → f
  3. Intersect(g, f) → C
  4. Vector(C, B) → u
  5. OrthogonalVector(u) → v
  6. Mirror(E, g) → E'
  7. Line(U, f) → j_1
  8. OrthogonalLine(I_1, j_1) → p_1
  9. Midpoint(A, C) → D
  10. Rotate(F, 90°, D) → F'
  11. Midpoint(F', D) → L
  12. Line(M, f) → q
  13. Line(C_1, q) → n_1
  14. Intersect(p_1, n_1) → J_1
  15. Mirror(M, f) → M'
  16. Line(E', g) → b
  17. Line(I, f) → i
  18. Line(M', i) → l
  19. Intersect(b, l) → W
  20. Intersect(p_1, l) → K_1
  21. Circle(D, E) → c
  22. OrthogonalLine(D, f) → h
  23. Rotate(G, 90°, D) → G'
  24. CircleArc(D, F', E) → d
  25. CircleArc(D, G', F) → e
  26. Intersect(e, i) → J, K
  27. Polygon(G, H, I, K) → q1, g_1, h_1, i_1, k
  28. Mirror(L, f) → L'
  29. Line(N, i) → j
  30. Line(H, h) → m
  31. Intersect(m, l) → O
  32. Intersect(m, j) → P
  33. Polygon(M, L, L', M', O, P, N) → poly1, m_1, l_1, l', m', o_1, p, n
  34. Intersect(e, q) → Q,
  35. Intersect(d, e, 1) → R
  36. Midpoint(Q, L) → S
  37. Semicircle(S, T) → r
  38. Semicircle(T, S) → s
  39. CircleSector(D, F, F') → t
  40. Segment(S, T) → a
  41. Line(U, b) → f_1
  42. Line(V, f_1) → k_1
  43. Intersect(k_1, l) → Z
  44. Intersect(f_1, n_1) → E_1
  45. Polygon(E_1, C_1, W, Z, D_1, B_1) → poly2, e_1, c_1, w, z_1, d_1, b_1
  46. Line(H_1, p_1) → q_1
  47. Intersect(q_1, l) → V_1
  48. Polygon(P_1, Q_1, T_1, U_1, Z_1, W_1, V_1) → poly3, s_1, t_1, f_2, u_1, g_2, w_1, v_1
  49. LineBisector(K_1, Z_1) → h_2
  50. Intersect(h_2, f) → C_2
  51. LineBisector(U_1, O_1) → i_2
  52. Intersect(i_2, p_1) → J_2
  53. Polygon(R_1, S_1, N_1, J_1) → q2, j_2, k_2, l_2, m_2
  54. CircleSector(J_2, O_1, U_1) → d_2
  55. CircleSector(C_2, K_1, Z_1) → c_2
  56. Intersect(d_2, i_2) → G_2,
  57. Polygon(U_1, G_2, Z_1) → t1, n_2, p_2, q_2
  58. CurveCartesian(((1 - t)^(2) * S_1) + (((2 * (1 - t)) * t) * A_2) + (t^(2) * N_1), t, 0, 1) → b_2
  59. CurveCartesian(((1 - t)^(3) * N_1) + (((3 * (1 - t)^(2)) * t) * E_2) + (((3 * (1 - t)) * t^(2)) * L_2) + (t^(3) * O_1), t, 0, 1) → a_2
  60. CircleArc(J_2, O_1, U_1) → d_7
  61. CurveCartesian(((1 - t)^(3) * J_1) + (((3 * (1 - t)^(2)) * t) * L_1) + (((3 * (1 - t)) * t^(2)) * K_2) + (t^(3) * K_1), t, 0, 1) → a_1
  62. CurveCartesian(((1 - t)^(3) * R_1) + (((3 * (1 - t)^(2)) * t) * B_2) + (((3 * (1 - t)) * t^(2)) * D_2) + (t^(3) * J_1), t, 0, 1) → r_1
  63. Polygon(G_1, T_1, J_2, I_1) → q3, r_2, s_2, t_2, e_2
  64. Segment(F', G') → f_3
  65. Segment(F, H) → g_3
  66. Segment(N_1, I_1) → h_3