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Arco de Herradura: Geometric and Trigonometric Application

Arco de Herradura: Geometric and Trigonometric Application
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2023-03-17 21:42
CircleAngleVectorGeometric Construction
In collections geometriadinamica.es
This example demonstrates the application of geometry and trigonometry through geometric construction. Key mathematical concepts include triangles, circles, angles, and vectors. Construction involves GeoGebra commands such as Segment, Midpoint, Rotate, Circle, etc. Suitable for high school students or college undergraduates to learn basic geometry and trigonometry.

GeoGebra Commands & Parameters

  1. If(zz ≤ 0, 10, zz) → u
  2. Segment(D, B) → e
  3. Midpoint(C, D) → K
  4. Rotate(C, Max[(-ε), (((-(u - 2)) * ε) * 180 / 3.14 / (2°))], K) → C'_2
  5. Circle(K, C) → f_1
  6. Midpoint(C, D) → F
  7. Line(F, e) → k
  8. Intersect(f_1, k, 1) → L
  9. Circle(L, C'_2) → g_1
  10. Center(g_1) → O
  11. Intersect(f_1, g_1, 1) → M
  12. Mirror(M, k) → M'_1
  13. Midpoint(C, D) → E
  14. Segment(A, C) → d
  15. Segment(E, C) → f
  16. Rotate(C, Max[((-(c - 3)) * 180 / (5°)), 180°], E) → C'
  17. Rotate(C, 359.91000000000014°, E) → C''
  18. CircumcircleArc(C, C'', C') → g
  19. Segment(C', E) → h
  20. Segment(C, F) → r
  21. Mirror(D, k) → D'_1
  22. Intersect(f_1, g_1, 2) → N
  23. Intersect(g_1, k, 2) → P
  24. Angle(M, O, M'_1) → δ
  25. Segment(K, C) → h_1
  26. Segment(K, C'_2) → i_1
  27. CircleArc(K, C'_2, C) → k_1
  28. Mirror(C'_2, k) → Q
  29. Segment(K, Q) → l_1
  30. CircleArc(K, D, Q) → q_1
  31. CircumcircleArc(Q, O, M) → t_1
  32. Rotate(M, Min[δ / 2, ((u - 4) * δ / 8)], L) → R
  33. Rotate(C, (-ε), K) → C'_3
  34. Circle(L, C'_3) → p_1
  35. CircleArc(L, M, R) → r_1
  36. Segment(L, R) → j_1
  37. Mirror(L, k) → L'
  38. Mirror(R, k) → R'
  39. Segment(L', R') → m_1
  40. Mirror(L, k) → L'_1
  41. Mirror(M, k) → M'
  42. Mirror(R, k) → R'_1
  43. Arc(Mirror[Circle[L, M], k], M', R'_1) → s_1
  44. Circle(K, C) → c_2
  45. Segment(T, T1) → n_1
  46. Mirror(D, n_1) → D'_2
  47. Mirror(B, n_1) → B'
  48. Segment(D'_2, B') → e'
  49. Mirror(A, n_1) → A'
  50. Mirror(C, n_1) → C'_4
  51. Segment(A', C'_4) → d'
  52. Vector(A, B') → z
  53. Translate(pic1, z) → pic1'
  54. Translate(pic1, z) → pic1'_1

AI Drawing Prompt Reference

Draw a horseshoe arch formed by two intersecting circles and auxiliary lines. Start with a horizontal segment as the base, find its midpoint, and draw a large circle centered there. Construct a rotated point above the base to define the arch's starting arc. Then draw a smaller circle with another center, intersecting the large circle, and use reflection and rotation to create the symmetric arch outline. Connect key points to form triangles and segments, mark an angle, and add multiple arcs and auxiliary lines to complete the geometric and trigonometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.