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Dynamic Geometry: Antonio Gutierrez's Theorem

Dynamic Geometry: Antonio Gutierrez's Theorem
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2017-04-03 09:38
FunctionCoordinate GeometryGeometric Construction
This example dynamically illustrates a theorem by Antonio Gutierrez, showcasing its applicability through adjustable parameters. Core math concepts include variance, planes, quadratic equations, indefinite integrals, and expected value. Construction highlights the use of commands like Rotate, Segment, LineBisector, and Dilate, along with objects such as Points and Lines, to build intricate geometric figures. Suitable for high school and above, helping learners grasp complex geometric theorems visually and understand parameter effects.

GeoGebra Commands & Parameters

  1. Rotate(A, (-((a * π / 180))), B) → A'
  2. Angle(A', B, A) → α
  3. Segment(A, B) → f
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Segment(A, C) → h
  7. Segment(B, C) → i
  8. LineBisector(i) → j
  9. LineBisector(f) → k
  10. Line(A, B) → m
  11. OrthogonalLine(C, m) → n
  12. Intersect(m, n) → E
  13. Angle(E, C, A) → γ
  14. Angle(E, A, C) → ε
  15. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], E) → C'_1
  16. Dilate(B, If[3 < o ≤ 4, 4 - o, 0], E) → B'
  17. Midpoint(A, B) → J
  18. Segment(A, E) → g_1
  19. Segment(A, J) → h_1
  20. Min(f, i) → u
  21. Circle(B, (0.2 * u)) → r_1
  22. Intersect(r_1, f) → K,
  23. Intersect(r_1, i) → L,
  24. CircleSector(B, L, K) → s_1
  25. Point(f) → M
  26. Segment(C, M) → p
  27. Line(C, M) → q
  28. OrthogonalLine(A, q) → r
  29. Intersect(q, r) → N
  30. Line(C, B) → s
  31. OrthogonalLine(A, s) → c
  32. Intersect(s, c) → O
  33. Line(N, O) → e
  34. OrthogonalLine(C, e) → i_1
  35. Intersect(e, i_1) → P
  36. Angle(A, C, M) → θ
  37. Angle(O, C, P) → ι
  38. Segment(C, P) → j_1
  39. Min({h, p, i, j_1}) → v
  40. Circle(C, (0.4 * v)) → c_1
  41. Intersect(c_1, h) → Q,
  42. Intersect(c_1, p) → R,
  43. CircleSector(C, Q, R) → d_1
  44. Dilate(C, If[0 < o ≤ 1, 1 - o, 0], M) → C'_2
  45. Segment(C, C'_2) → t
  46. Angle(M, N, A) → κ_1
  47. Dilate(M, If[1 < o ≤ 2, 2 - o, 0], N) → M'
  48. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], N) → A'_1
  49. Segment(M, M') → f_1
  50. Segment(A, A'_1) → k_1
  51. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], O) → A'_2
  52. Segment(A, A'_2) → l_1
  53. Dilate(N, If[3 < o ≤ 4, 4 - o, 0], O) → N'
  54. Segment(N, N') → m_1
  55. Dilate(O, If[4 < o ≤ 5, 5 - o, 0], P) → O'
  56. Dilate(C, If[4 < o ≤ 5, 5 - o, 0], P) → C'_3
  57. Angle(C, P, O) → ζ
  58. Segment(O, O') → n_1
  59. Segment(C, C'_3) → p_1
  60. Rotate(Q, If[5 < o ≤ 6, ((o - 5) * θ), θ], C) → Q'
  61. CircleSector(C, Q, Q') → e_1
  62. Angle(A, C, B) → κ
  63. Polygon(A, B, C) → poly1, c_2, a_1, b
  64. Rotate(d_1, If[6.5 < o ≤ 7.5, ((o - 6.5) * κ), κ], C) → q_1
  65. Circle(B, 1) → d
  66. Circle(C, 1) → t_1
  67. Intersect(d, s) → D, F
  68. Intersect(t_1, s) → G, H
  69. Ray(B, F) → l
  70. Ray(C, G) → b_1
  71. Angle(C, O, A) → β

AI Drawing Prompt Reference

Draw a dynamic geometric illustration of Antonio Gutierrez's theorem with adjustable parameters. Include points and line segments that are rotated and scaled to generate multiple auxiliary points and lines. Construct angle bisectors of two line segments and find their intersection point. Draw perpendicular lines and circles centered at the intersection point relative to the line segments. Use these geometric objects to build intricate figures, showing how parameter changes affect the shape.
The prompt above was compiled from the original drawing commands and is for reference only.