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GeoGebra Logo GOL TV

GeoGebra Logo GOL TV
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2019-10-09 19:54
CircleVectorFunctionCoordinate GeometryGeometric Construction
This example demonstrates the geometric construction of the Logo GOL TV using GeoGebra software. It involves core mathematical concepts such as angles, circles, geometry, function graphs, mathematics, squares, polynomial functions, upper and lower sum or Riemann sum, tangent lines or tangents, and quadratic equations. The construction utilizes GeoGebra commands and objects like Line, Vector, OrthogonalLine, OrthogonalVector, Midpoint, Mirror, Intersect, Polygon, Semicircle, LineBisector, and CircleArc. It is suitable for high school students learning geometric constructions and function graphs.

GeoGebra Commands & Parameters

  1. Line(A, B) → m
  2. Vector(A, B) → u
  3. OrthogonalLine(N, m) → n
  4. OrthogonalVector(u) → v
  5. Line(F, m) → h
  6. Midpoint(E, B) → D
  7. Mirror(h, D) → h'
  8. Intersect(n, h') → U_1
  9. Line(D, h') → j
  10. Line(A_2, j) → q_2
  11. Intersect(n, q_2) → J_2
  12. Line(E, m) → f
  13. OrthogonalLine(B, f) → g
  14. Intersect(g, f) → C
  15. OrthogonalLine(G, m) → i
  16. Mirror(i, D) → i'
  17. Intersect(i, h') → I
  18. Polygon(E, C, B, A) → q2, e, c, b, a
  19. OrthogonalLine(D, j) → k
  20. OrthogonalLine(H, m) → l
  21. Intersect(h, i) → P
  22. Mirror(Q, j) → Q'
  23. Line(R, j) → p
  24. Mirror(p, j) → p'
  25. OrthogonalLine(Q', p') → q
  26. Intersect(q, p) → S
  27. Intersect(l, j) → Z
  28. Mirror(S, j) → S'
  29. Semicircle(Q, Q') → d
  30. Intersect(i, p') → K
  31. Line(J', j) → r
  32. Line(V, B_1) → s
  33. Intersect(s, r) → M
  34. Polygon(Q', W', Q, L, A_1, T, V, M, J', Z, W) → poly1, t, m_2, n_2, j_1, l_1, m_1, q_1, a_1, j_2, k_2, l_2
  35. OrthogonalLine(U, j) → f_1
  36. Intersect(f_1, h') → C_1
  37. Mirror(C_1, j) → D_1
  38. Semicircle(D_1, C_1) → c_1
  39. Mirror(c_1, k) → d_1
  40. Mirror(d_1, j) → e_1
  41. Mirror(E_1, D) → G_1
  42. Mirror(F_1, D) → H_1
  43. Polygon(E_1, F_1, G_1, H_1) → q1, g_1, h_1, i_1, k_1
  44. Mirror(C_1, k) → I_1
  45. Polygon(C_1, I_1, F_1, E_1, H_1, D_1) → poly2, n_1, p_1, r_1, s_1, t_1, p_2
  46. Mirror(C_1, D) → J_1
  47. Mirror(I_1, D) → K_1
  48. Mirror(F_1, D) → L_1
  49. Mirror(E_1, D) → M_1
  50. Mirror(H_1, D) → N_1
  51. Mirror(C_1, D) → O_1
  52. Mirror(I_1, D) → P_1
  53. Mirror(F_1, D) → Q_1
  54. Mirror(E_1, D) → R_1
  55. Mirror(H_1, D) → S_1
  56. Mirror(D_1, D) → T_1
  57. Polygon(O_1, P_1, Q_1, R_1, S_1, T_1) → poly2', o_1, b_1, f_2, g_2, h_2, i_2
  58. Mirror(U_1, j) → V_1
  59. OrthogonalLine(Z_1, j) → r_2
  60. Intersect(r_2, q_2) → E_2
  61. Intersect(d_1, q_2) → F_2,
  62. Line(W_1, J_2) → s_2
  63. Intersect(d_1, s_2) → G_2, H_2
  64. Line(Z_1, s_2) → t_2
  65. Line(A_2, t_2) → a_2
  66. Intersect(t_2, q_2) → B_2
  67. Intersect(a_2, h) → C_2
  68. Polygon(W_1, Z_1, B_2, A_2, C_2, I_2, H_2) → poly3, w_1, z_1, b_2, c_2, d_2, e_2, f_3
  69. LineBisector(H_2, I_2) → g_3
  70. Intersect(g_3, j) → K_2
  71. CircleArc(K_2, H_2, I_2) → c_3

AI Drawing Prompt Reference

Draw a geometric logo composed of lines, perpendiculars, mirrored shapes, and semicircles. Start with a horizontal baseline and a vector along it, then construct perpendicular lines. Use a midpoint as symmetry center to mirror several lines, creating a symmetric grid. Within this grid, form multiple polygons including a rectangle and irregular quadrilaterals, and add semicircles and arcs as decorative elements. Ensure all parts maintain mirror symmetry, resembling a TV screen outline with internal details like intersections, parallel lines, and mirrored arcs.
The prompt above was compiled from the original drawing commands and is for reference only.