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Arcs

Arcs
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2023-03-13 22:08
CircleTrigonometryGeometric Construction
In collections geometriadinamica.es
This example demonstrates the construction of arcs. Key mathematical concepts include arcs, circles, and trigonometric functions. Using GeoGebra commands such as Segment, CircleArc, and Arc, arcs can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment(D, B) → e
  2. Midpoint(C, D) → K
  3. Rotate(C, Max[(-ε), (((-(u - 2)) * ε) * 180 / 3.14 / (2°))], K) → C'_2
  4. Circle(K, C) → f_1
  5. Midpoint(C, D) → F
  6. Line(F, e) → k
  7. Intersect(f_1, k, 1) → L
  8. Circle(L, C'_2) → g_1
  9. Center(g_1) → O
  10. Intersect(f_1, g_1, 1) → M
  11. Mirror(M, k) → M'_1
  12. Circle(F, i) → p
  13. Intersect(p, k, 2) → G
  14. Midpoint(C, D) → E
  15. Segment(A, C) → d
  16. Segment(E, C) → f
  17. Rotate(C, Max[((-(c - 3)) * 180 / (5°)), 180°], E) → C'
  18. Rotate(C, 359.91000000000014°, E) → C''
  19. CircumcircleArc(C, C'', C') → g
  20. Segment(C', E) → h
  21. Segment(G, C) → l
  22. If(zz < 0, 10, zz) → n
  23. Segment(C, F) → r
  24. Circle(C, m) → s
  25. Intersect(s, r, 1) → H
  26. Circle(H, D) → t
  27. Intersect(t, k) → I, J
  28. Angle(D, H, I) → β
  29. Segment(H, D) → a_1
  30. Rotate(D, Min[β, (((n - 3) * β) * 180 / 3.14 / (5°))], H) → D'
  31. Segment(H, D') → b_1
  32. CircleArc(H, D, D') → c_1
  33. Mirror(H, k) → H'
  34. Mirror(D', k) → D''
  35. Segment(H', D'') → d_1
  36. Mirror(H, k) → H'_1
  37. Mirror(D, k) → D'_1
  38. Mirror(D', k) → D''_1
  39. Arc(Mirror[Circle[H, D], k], D'_1, D''_1) → e_1
  40. Intersect(f_1, g_1, 2) → N
  41. Intersect(g_1, k, 2) → P
  42. Segment(K, C) → h_1
  43. Segment(K, C'_2) → i_1
  44. CircleArc(K, C'_2, C) → k_1
  45. Mirror(C'_2, k) → Q
  46. Segment(K, Q) → l_1
  47. CircleArc(K, D, Q) → q_1
  48. CircumcircleArc(Q, O, M) → t_1
  49. Rotate(C, (-ε), K) → C'_3
  50. Circle(L, C'_3) → p_1
  51. Mirror(L, k) → L'
  52. Mirror(L, k) → L'_1
  53. Mirror(M, k) → M'
  54. Circle(K, C) → c_2
  55. Segment(T1, T) → n_1
  56. Mirror(D, n_1) → D'_2
  57. Mirror(B, n_1) → B'
  58. Segment(D'_2, B') → e'
  59. Mirror(A, n_1) → A'
  60. Mirror(C, n_1) → C'_4
  61. Segment(A', C'_4) → d'
  62. Vector(A, B') → z
  63. Translate(pic1, z) → pic1'
  64. Translate(pic1, z) → pic1'_1

AI Drawing Prompt Reference

Create a geometric figure featuring multiple intersecting circles and arcs. Start with a segment DB and its midpoint K, then draw circle f1 centered at K. Draw another line through the midpoint of CD intersecting circle f1 at point L, then create circle g1 centered at L. The two circles intersect at points M and N. Use the perpendicular bisector of CD as an axis of symmetry to create mirrored points. Rotate point C around point E to generate points C' and C'', then construct a circular arc through these three points. Similarly, create an arc centered at H with radius DH, then mirror it to create symmetric arcs. Complete the figure by drawing multiple segments and arcs between various intersection points to form a symmetric pattern of circular arcs.
The prompt above was compiled from the original drawing commands and is for reference only.