MathPlotAI Logo MathPlotAI

Giugiuc Parabola

Giugiuc Parabola
Loading the math board and drawing, please wait…
2016-08-20 06:22
CircleGeometric Construction
This example demonstrates the geometric construction of the Giugiuc parabola. Key mathematical concepts include parabola, circumcircle, rectangle, correlation, parallelogram, and equilateral triangles. Using GeoGebra commands such as Line, Parabola, Point, Tangent, Intersect, Polygon, Circle, Center, Segment, Angle, Distance, and OrthogonalLine, complex geometric figures can be constructed. Suitable for high school mathematics education and research.

GeoGebra Commands & Parameters

  1. Line(A_4, B_4) → a_3
  2. Parabola(F, a_3) → c_3
  3. Point(c_3) → B_1
  4. Point(c_3) → A_1
  5. Point(c_3) → C_1
  6. Tangent(B_1, c_3) → b_3,
  7. Tangent(A_1, c_3) → d,
  8. Tangent(C_1, c_3) → e,
  9. Intersect(b_3, e) → A
  10. Intersect(d, e) → B
  11. Intersect(b_3, d) → C
  12. Polygon(C, A, B) → poligon1, i, g, h
  13. Circle(A, B_1, C_1) → f
  14. Circle(B, C_1, A_1) → k
  15. Center(f) → A_2
  16. Center(k) → B_2
  17. Circle(C, A_1, B_1) → p
  18. Center(p) → C_2
  19. Segment(C, B) → j
  20. Point(b_3) → D
  21. Segment(A, D) → l
  22. Point(e) → E
  23. Segment(A, E) → m
  24. Point(k) → G
  25. Segment(B_2, G) → n
  26. Point(p) → H_1
  27. Segment(C_2, H_1) → q
  28. Point(f) → I
  29. Segment(A_2, I) → r
  30. Polygon(A_2, C_2, B_2) → poligon2, b_2, a_2, c_2
  31. Angle(A_2, B_2, C_2) → α
  32. Distance(A_2, C_2) → distanceA2C2
  33. Distance(A, C) → distanceAC
  34. Distance(F, a_3) → distanceFa
  35. Distance(A, B) → distanceAB
  36. Distance(A_2, B_2) → distanceA2B2
  37. OrthogonalLine(C_1, m) → t
  38. OrthogonalLine(B_1, i) → a_1
  39. OrthogonalLine(A_1, h) → b_1
  40. Intersect(t, b_1) → B_3
  41. Intersect(a_1, t) → A_3
  42. Intersect(b_1, a_1) → C_3
  43. Distance(A_3, C_3) → distanceKL
  44. Distance(A_2, C_2) → o
  45. Distance(B_3, C_3) → distanceJL
  46. Distance(B_2, C_2) → distanceB2C2
  47. Distance(B, C) → distanceBC
  48. Distance(A, C) → u
  49. Distance(C_3, B_3) → distanceLJ
  50. Distance(A_3, C_3) → v
  51. Line(A, A_2) → c_1
  52. Line(C, C_2) → d_1
  53. Line(B, B_2) → e_1
  54. Polygon(C_3, A_3, B_3) → poly1, j_1, l_1, k_1
  55. Angle(h, b_1) → β
  56. Angle(l, a_1) → γ
  57. Angle(m, t) → δ
  58. Distance(C_2, C_3) → distanceC2C3
  59. Distance(C_2, C) → distanceC2C
  60. Distance(B, B_2) → distanceBB2
  61. Distance(B_2, B_3) → distanceB2B3
  62. Distance(A, F) → distanceAF
  63. Distance(F, A_3) → distanceFA3
  64. Segment(C, C_3) → f_1
  65. Segment(A_1, B_3) → a
  66. Segment(C_1, B_3) → c
  67. Segment(B, B_3) → i_1
  68. Segment(A, A_3) → m_1
  69. Segment(B_1, A_3) → b