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Triangle to Conic

Triangle to Conic
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2016-09-11 08:35
TriangleCircleGeometric Construction
This example demonstrates how to construct conic sections using the vertices and sides of a triangle. It involves core mathematical concepts such as conic sections (circle, ellipse, hyperbola, parabola), functions, differential equations, and quadratic equations. Key GeoGebra commands/objects used include Line, Rotate, Angle, Ray, Point, Segment, Polygon, PointIn, Intersect, Conic, Focus, Vertex, Min, Circle, CircleSector, Dilate, Vector, and Translate. Suitable for high school students and above to understand the geometric construction of conic sections.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Segment(C, B) → h
  7. Polygon(A, B, C) → poly1, c, a, b
  8. PointIn(poly1) → D
  9. Line(D, f) → i
  10. Line(D, h) → j
  11. Line(D, g) → k
  12. Intersect(k, h) → E
  13. Intersect(f, k) → F
  14. Intersect(i, g) → G
  15. Intersect(j, g) → H
  16. Intersect(h, i) → I
  17. Intersect(f, j) → J
  18. Conic(F, J, I, E, H) → d
  19. Focus(d) → K, L
  20. Vertex(d) → M, N, O, P
  21. Segment(A, B) → l
  22. Segment(C, A) → m
  23. Min({l, m, h}) → e
  24. Circle(A, (0.15 * e)) → p
  25. Circle(C, (0.15 * e)) → q
  26. Circle(B, (0.15 * e)) → r
  27. Intersect(q, m, 1) → Q
  28. Intersect(q, h, 1) → R
  29. Intersect(p, l, 1) → S
  30. Intersect(p, m, 1) → T
  31. Intersect(r, l, 1) → U
  32. Intersect(r, h, 1) → V
  33. CircleSector(C, Q, R) → s
  34. CircleSector(A, S, T) → t
  35. CircleSector(B, V, U) → c_1
  36. Dilate(D, If[0 < n ≤ 1, 1 - n, 0], I) → D'
  37. Dilate(D, If[0 < n ≤ 1, 1 - n, 0], G) → D'_1
  38. Segment(D, D') → f_1
  39. Segment(D, D'_1) → g_1
  40. Dilate(A, If[1 < n ≤ 2, 2 - n, 0], G) → A'
  41. Vector(A, A') → u
  42. Translate(t, u) → t'
  43. CircleArc(A, S, T) → d_1
  44. Dilate(D, If[2 < n ≤ 3, 3 - n, 0], E) → D'_2
  45. Dilate(D, If[2 < n ≤ 3, 3 - n, 0], F) → D'_3
  46. Segment(D, D'_2) → h_1
  47. Segment(D, D'_3) → i_1
  48. Dilate(C, If[3 < n ≤ 4, 4 - n, 0], E) → C'
  49. Vector(C, C') → v
  50. Translate(s, v) → s'
  51. CircleArc(C, Q, R) → e_1
  52. Dilate(D, If[4 < n ≤ 5, 5 - n, 0], J) → D'_4
  53. Dilate(D, If[4 < n ≤ 5, 5 - n, 0], H) → D'_5
  54. Segment(D, D'_4) → j_1
  55. Segment(D, D'_5) → k_1
  56. Dilate(B, If[5 < n ≤ 6, 6 - n, 0], J) → B'_1
  57. Vector(B, B'_1) → w
  58. Translate(c_1, w) → p_1
  59. CircleArc(B, V, U) → q_1