Approximating Pi Using S. Ramanujan's Method

Approximating Pi Using S. Ramanujan's Method
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2020-02-02 21:45
This example demonstrates S. Ramanujan's method for approximating the value of pi. Key mathematical concepts include sequences and limits. The construction process, involving commands like Point, Circle, Intersect, etc., is explained in the construction summary. Suitable for high school mathematics education and learning about sequences and limits.

GeoGebra Commands & Parameters

  1. Point(yAxis) → O
  2. Circle(O, 1) → c
  3. Point(c) → A
  4. Line(A, O) → f
  5. Intersect(c, f, 2) → B
  6. Segment(A, B) → t
  7. OrthogonalLine(O, f) → g
  8. Intersect(c, g, 2) → C
  9. Rotate(O, (-(15°)), A) → O'
  10. Angle(O', A, O) → α
  11. Ray(A, O') → h
  12. Circle(A, 0.3) → d
  13. Intersect(d, h, 1) → D
  14. Circle(D, A) → e
  15. Intersect(e, h, 2) → E
  16. Circle(E, D) → k
  17. Intersect(k, h, 2) → F
  18. ArcoyPunto(A, D) → p
  19. ArcoyPunto(D, E) → q
  20. ArcoyPunto(E, F) → r
  21. Segment(F, O) → i
  22. Line(D, i) → j
  23. Intersect(j, t) → T
  24. Segment(B, C) → l
  25. Circle(C, Segment[A, T]) → s
  26. Intersect(s, l, 1) → M
  27. ArcoyPunto(C, M) → d_1
  28. Circle(M, C) → c_1
  29. Intersect(c_1, l, 2) → N
  30. ArcoyPunto(M, N) → e_1
  31. Segment(A, M) → m
  32. Segment(A, N) → n
  33. Circle(A, M) → f_1
  34. Intersect(f_1, n, 1) → P
  35. CircleArc(A, P, M) → g_1
  36. Line(P, l) → b
  37. Intersect(b, m) → Q
  38. Segment(Q, P) → s_1
  39. Segment(O, Q) → h_1
  40. Line(T, h_1) → i_1
  41. Intersect(i_1, m) → R
  42. Segment(T, R) → j_1
  43. Tangent(A, c) → k_1,
  44. Circle(A, R) → p_1
  45. Intersect(p_1, k_1, 1) → S
  46. Segment(A, S) → m_1
  47. CircleArc(A, S, R) → q_1
  48. Segment(O, S) → l_1
  49. Polygon(A, R, T) → V1, t_1, a, r_1
  50. Polygon(A, Q, O) → V2, o, a_1, q_2
  51. Polygon(A, Q, P) → V3, p_2, a_2, q_3
  52. Polygon(A, M, N) → V4, n_1, a_3, m_2
  53. Polygon(A, N, B) → V5, b_1, a_4, n_2
  54. Angle(N, B, A) → β
  55. Polygon(A, M, B) → V6, b_2, a_5, m_3

AI Drawing Prompt Reference

Draw a unit circle centered at the origin, then use a series of rotations, intersections, and arcs to approximate the value of pi. Start by drawing the unit circle and its diameter, then find a series of points through rotations and intersections, and finally construct arcs using these points to form a geometric figure that approximates pi.
The prompt above was compiled from the original drawing commands and is for reference only.