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Recamán's Sequence II

Recamán's Sequence II
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2018-11-27 12:19
FunctionSequenceCoordinate Geometry
In collections Graphs of Sequences
This example demonstrates the generation process of Recamán's sequence, a fascinating sequence defined based on the difference between the previous term and the current term. Using GeoGebra commands such as Sequence, Mod, If, Length, etc., the sequence can be dynamically generated and observed for its pattern. Suitable for high school mathematics education and research.

GeoGebra Commands & Parameters

  1. Sequence(Element[Seq, i], i, 1, n + 1) → Seq2
  2. Mod(n, 2) → test
  3. If(test ≟ 1, (2 * π), π) → umax
  4. If(test ≟ 1, π, 0) → umin
  5. Length(Seq) → lng
  6. CurveCartesian((radArc * cos(u)) + mid, (radArc * sin(u)), u, umin, umax) → curveSeq
  7. If(n < 5, Element[Seq, 4], Max[Seq2]) → lastElement
  8. Element(Seq, n) → n1
  9. Element(Seq, n + 1) → n2
  10. CurveCartesian((abs((Element[Seq, 2] - Element[Seq, 1]) / 2) * cos(u)) + (Element[Seq, 2] + Element[Seq, 1]) / 2, (abs((Element[Seq, 2] - Element[Seq, 1]) / 2) * sin(u)), u, If[Mod[1, 2] ≟ 1, π, 0], If[Mod[1, 2] ≟ 1, (2 * π), π]) → B1
  11. CurveCartesian((abs((Element[Seq, 3] - Element[Seq, 2]) / 2) * cos(u)) + (Element[Seq, 3] + Element[Seq, 2]) / 2, (abs((Element[Seq, 3] - Element[Seq, 2]) / 2) * sin(u)), u, If[Mod[2, 2] ≟ 1, π, 0], If[Mod[2, 2] ≟ 1, (2 * π), π]) → B2
  12. CurveCartesian((abs((Element[Seq, 4] - Element[Seq, 3]) / 2) * cos(u)) + (Element[Seq, 4] + Element[Seq, 3]) / 2, (abs((Element[Seq, 4] - Element[Seq, 3]) / 2) * sin(u)), u, If[Mod[3, 2] ≟ 1, π, 0], If[Mod[3, 2] ≟ 1, (2 * π), π]) → B3
  13. CurveCartesian((abs((Element[Seq, 5] - Element[Seq, 4]) / 2) * cos(u)) + (Element[Seq, 5] + Element[Seq, 4]) / 2, (abs((Element[Seq, 5] - Element[Seq, 4]) / 2) * sin(u)), u, If[Mod[4, 2] ≟ 1, π, 0], If[Mod[4, 2] ≟ 1, (2 * π), π]) → B4
  14. CurveCartesian((abs((Element[Seq, 6] - Element[Seq, 5]) / 2) * cos(u)) + (Element[Seq, 6] + Element[Seq, 5]) / 2, (abs((Element[Seq, 6] - Element[Seq, 5]) / 2) * sin(u)), u, If[Mod[5, 2] ≟ 1, π, 0], If[Mod[5, 2] ≟ 1, (2 * π), π]) → B5
  15. CurveCartesian((abs((Element[Seq, 7] - Element[Seq, 6]) / 2) * cos(u)) + (Element[Seq, 7] + Element[Seq, 6]) / 2, (abs((Element[Seq, 7] - Element[Seq, 6]) / 2) * sin(u)), u, If[Mod[6, 2] ≟ 1, π, 0], If[Mod[6, 2] ≟ 1, (2 * π), π]) → B6
  16. CurveCartesian((abs((Element[Seq, 8] - Element[Seq, 7]) / 2) * cos(u)) + (Element[Seq, 8] + Element[Seq, 7]) / 2, (abs((Element[Seq, 8] - Element[Seq, 7]) / 2) * sin(u)), u, If[Mod[7, 2] ≟ 1, π, 0], If[Mod[7, 2] ≟ 1, (2 * π), π]) → B7
  17. CurveCartesian((abs((Element[Seq, 9] - Element[Seq, 8]) / 2) * cos(u)) + (Element[Seq, 9] + Element[Seq, 8]) / 2, (abs((Element[Seq, 9] - Element[Seq, 8]) / 2) * sin(u)), u, If[Mod[8, 2] ≟ 1, π, 0], If[Mod[8, 2] ≟ 1, (2 * π), π]) → B8
  18. CurveCartesian((abs((Element[Seq, 10] - Element[Seq, 9]) / 2) * cos(u)) + (Element[Seq, 10] + Element[Seq, 9]) / 2, (abs((Element[Seq, 10] - Element[Seq, 9]) / 2) * sin(u)), u, If[Mod[9, 2] ≟ 1, π, 0], If[Mod[9, 2] ≟ 1, (2 * π), π]) → B9
  19. CurveCartesian((abs((Element[Seq, 11] - Element[Seq, 10]) / 2) * cos(u)) + (Element[Seq, 11] + Element[Seq, 10]) / 2, (abs((Element[Seq, 11] - Element[Seq, 10]) / 2) * sin(u)), u, If[Mod[10, 2] ≟ 1, π, 0], If[Mod[10, 2] ≟ 1, (2 * π), π]) → B10
  20. CurveCartesian((abs((Element[Seq, 12] - Element[Seq, 11]) / 2) * cos(u)) + (Element[Seq, 12] + Element[Seq, 11]) / 2, (abs((Element[Seq, 12] - Element[Seq, 11]) / 2) * sin(u)), u, If[Mod[11, 2] ≟ 1, π, 0], If[Mod[11, 2] ≟ 1, (2 * π), π]) → B11
  21. CurveCartesian((abs((Element[Seq, 13] - Element[Seq, 12]) / 2) * cos(u)) + (Element[Seq, 13] + Element[Seq, 12]) / 2, (abs((Element[Seq, 13] - Element[Seq, 12]) / 2) * sin(u)), u, If[Mod[12, 2] ≟ 1, π, 0], If[Mod[12, 2] ≟ 1, (2 * π), π]) → B12
  22. CurveCartesian((abs((Element[Seq, 14] - Element[Seq, 13]) / 2) * cos(u)) + (Element[Seq, 14] + Element[Seq, 13]) / 2, (abs((Element[Seq, 14] - Element[Seq, 13]) / 2) * sin(u)), u, If[Mod[13, 2] ≟ 1, π, 0], If[Mod[13, 2] ≟ 1, (2 * π), π]) → B13
  23. CurveCartesian((abs((Element[Seq, 15] - Element[Seq, 14]) / 2) * cos(u)) + (Element[Seq, 15] + Element[Seq, 14]) / 2, (abs((Element[Seq, 15] - Element[Seq, 14]) / 2) * sin(u)), u, If[Mod[14, 2] ≟ 1, π, 0], If[Mod[14, 2] ≟ 1, (2 * π), π]) → B14
  24. CurveCartesian((abs((Element[Seq, 16] - Element[Seq, 15]) / 2) * cos(u)) + (Element[Seq, 16] + Element[Seq, 15]) / 2, (abs((Element[Seq, 16] - Element[Seq, 15]) / 2) * sin(u)), u, If[Mod[15, 2] ≟ 1, π, 0], If[Mod[15, 2] ≟ 1, (2 * π), π]) → B15
  25. CurveCartesian((abs((Element[Seq, 17] - Element[Seq, 16]) / 2) * cos(u)) + (Element[Seq, 17] + Element[Seq, 16]) / 2, (abs((Element[Seq, 17] - Element[Seq, 16]) / 2) * sin(u)), u, If[Mod[16, 2] ≟ 1, π, 0], If[Mod[16, 2] ≟ 1, (2 * π), π]) → B16
  26. CurveCartesian((abs((Element[Seq, 18] - Element[Seq, 17]) / 2) * cos(u)) + (Element[Seq, 18] + Element[Seq, 17]) / 2, (abs((Element[Seq, 18] - Element[Seq, 17]) / 2) * sin(u)), u, If[Mod[17, 2] ≟ 1, π, 0], If[Mod[17, 2] ≟ 1, (2 * π), π]) → B17
  27. CurveCartesian((abs((Element[Seq, 19] - Element[Seq, 18]) / 2) * cos(u)) + (Element[Seq, 19] + Element[Seq, 18]) / 2, (abs((Element[Seq, 19] - Element[Seq, 18]) / 2) * sin(u)), u, If[Mod[18, 2] ≟ 1, π, 0], If[Mod[18, 2] ≟ 1, (2 * π), π]) → B18
  28. CurveCartesian((abs((Element[Seq, 20] - Element[Seq, 19]) / 2) * cos(u)) + (Element[Seq, 20] + Element[Seq, 19]) / 2, (abs((Element[Seq, 20] - Element[Seq, 19]) / 2) * sin(u)), u, If[Mod[19, 2] ≟ 1, π, 0], If[Mod[19, 2] ≟ 1, (2 * π), π]) → B19
  29. CurveCartesian((abs((Element[Seq, 21] - Element[Seq, 20]) / 2) * cos(u)) + (Element[Seq, 21] + Element[Seq, 20]) / 2, (abs((Element[Seq, 21] - Element[Seq, 20]) / 2) * sin(u)), u, If[Mod[20, 2] ≟ 1, π, 0], If[Mod[20, 2] ≟ 1, (2 * π), π]) → B20
  30. CurveCartesian((abs((Element[Seq, 22] - Element[Seq, 21]) / 2) * cos(u)) + (Element[Seq, 22] + Element[Seq, 21]) / 2, (abs((Element[Seq, 22] - Element[Seq, 21]) / 2) * sin(u)), u, If[Mod[21, 2] ≟ 1, π, 0], If[Mod[21, 2] ≟ 1, (2 * π), π]) → B21
  31. CurveCartesian((abs((Element[Seq, 23] - Element[Seq, 22]) / 2) * cos(u)) + (Element[Seq, 23] + Element[Seq, 22]) / 2, (abs((Element[Seq, 23] - Element[Seq, 22]) / 2) * sin(u)), u, If[Mod[22, 2] ≟ 1, π, 0], If[Mod[22, 2] ≟ 1, (2 * π), π]) → B22
  32. CurveCartesian((abs((Element[Seq, 24] - Element[Seq, 23]) / 2) * cos(u)) + (Element[Seq, 24] + Element[Seq, 23]) / 2, (abs((Element[Seq, 24] - Element[Seq, 23]) / 2) * sin(u)), u, If[Mod[23, 2] ≟ 1, π, 0], If[Mod[23, 2] ≟ 1, (2 * π), π]) → B23
  33. CurveCartesian((abs((Element[Seq, 25] - Element[Seq, 24]) / 2) * cos(u)) + (Element[Seq, 25] + Element[Seq, 24]) / 2, (abs((Element[Seq, 25] - Element[Seq, 24]) / 2) * sin(u)), u, If[Mod[24, 2] ≟ 1, π, 0], If[Mod[24, 2] ≟ 1, (2 * π), π]) → B24
  34. CurveCartesian((abs((Element[Seq, 26] - Element[Seq, 25]) / 2) * cos(u)) + (Element[Seq, 26] + Element[Seq, 25]) / 2, (abs((Element[Seq, 26] - Element[Seq, 25]) / 2) * sin(u)), u, If[Mod[25, 2] ≟ 1, π, 0], If[Mod[25, 2] ≟ 1, (2 * π), π]) → B25
  35. CurveCartesian((abs((Element[Seq, 27] - Element[Seq, 26]) / 2) * cos(u)) + (Element[Seq, 27] + Element[Seq, 26]) / 2, (abs((Element[Seq, 27] - Element[Seq, 26]) / 2) * sin(u)), u, If[Mod[26, 2] ≟ 1, π, 0], If[Mod[26, 2] ≟ 1, (2 * π), π]) → B26
  36. CurveCartesian((abs((Element[Seq, 28] - Element[Seq, 27]) / 2) * cos(u)) + (Element[Seq, 28] + Element[Seq, 27]) / 2, (abs((Element[Seq, 28] - Element[Seq, 27]) / 2) * sin(u)), u, If[Mod[27, 2] ≟ 1, π, 0], If[Mod[27, 2] ≟ 1, (2 * π), π]) → B27
  37. CurveCartesian((abs((Element[Seq, 29] - Element[Seq, 28]) / 2) * cos(u)) + (Element[Seq, 29] + Element[Seq, 28]) / 2, (abs((Element[Seq, 29] - Element[Seq, 28]) / 2) * sin(u)), u, If[Mod[28, 2] ≟ 1, π, 0], If[Mod[28, 2] ≟ 1, (2 * π), π]) → B28
  38. CurveCartesian((abs((Element[Seq, 30] - Element[Seq, 29]) / 2) * cos(u)) + (Element[Seq, 30] + Element[Seq, 29]) / 2, (abs((Element[Seq, 30] - Element[Seq, 29]) / 2) * sin(u)), u, If[Mod[29, 2] ≟ 1, π, 0], If[Mod[29, 2] ≟ 1, (2 * π), π]) → B29
  39. CurveCartesian((abs((Element[Seq, 31] - Element[Seq, 30]) / 2) * cos(u)) + (Element[Seq, 31] + Element[Seq, 30]) / 2, (abs((Element[Seq, 31] - Element[Seq, 30]) / 2) * sin(u)), u, If[Mod[30, 2] ≟ 1, π, 0], If[Mod[30, 2] ≟ 1, (2 * π), π]) → B30
  40. CurveCartesian((abs((Element[Seq, 32] - Element[Seq, 31]) / 2) * cos(u)) + (Element[Seq, 32] + Element[Seq, 31]) / 2, (abs((Element[Seq, 32] - Element[Seq, 31]) / 2) * sin(u)), u, If[Mod[31, 2] ≟ 1, π, 0], If[Mod[31, 2] ≟ 1, (2 * π), π]) → B31
  41. CurveCartesian((abs((Element[Seq, 33] - Element[Seq, 32]) / 2) * cos(u)) + (Element[Seq, 33] + Element[Seq, 32]) / 2, (abs((Element[Seq, 33] - Element[Seq, 32]) / 2) * sin(u)), u, If[Mod[32, 2] ≟ 1, π, 0], If[Mod[32, 2] ≟ 1, (2 * π), π]) → B32
  42. CurveCartesian((abs((Element[Seq, 34] - Element[Seq, 33]) / 2) * cos(u)) + (Element[Seq, 34] + Element[Seq, 33]) / 2, (abs((Element[Seq, 34] - Element[Seq, 33]) / 2) * sin(u)), u, If[Mod[33, 2] ≟ 1, π, 0], If[Mod[33, 2] ≟ 1, (2 * π), π]) → B33
  43. CurveCartesian((abs((Element[Seq, 35] - Element[Seq, 34]) / 2) * cos(u)) + (Element[Seq, 35] + Element[Seq, 34]) / 2, (abs((Element[Seq, 35] - Element[Seq, 34]) / 2) * sin(u)), u, If[Mod[34, 2] ≟ 1, π, 0], If[Mod[34, 2] ≟ 1, (2 * π), π]) → B34
  44. CurveCartesian((abs((Element[Seq, 36] - Element[Seq, 35]) / 2) * cos(u)) + (Element[Seq, 36] + Element[Seq, 35]) / 2, (abs((Element[Seq, 36] - Element[Seq, 35]) / 2) * sin(u)), u, If[Mod[35, 2] ≟ 1, π, 0], If[Mod[35, 2] ≟ 1, (2 * π), π]) → B35
  45. CurveCartesian((abs((Element[Seq, 37] - Element[Seq, 36]) / 2) * cos(u)) + (Element[Seq, 37] + Element[Seq, 36]) / 2, (abs((Element[Seq, 37] - Element[Seq, 36]) / 2) * sin(u)), u, If[Mod[36, 2] ≟ 1, π, 0], If[Mod[36, 2] ≟ 1, (2 * π), π]) → B36
  46. CurveCartesian((abs((Element[Seq, 38] - Element[Seq, 37]) / 2) * cos(u)) + (Element[Seq, 38] + Element[Seq, 37]) / 2, (abs((Element[Seq, 38] - Element[Seq, 37]) / 2) * sin(u)), u, If[Mod[37, 2] ≟ 1, π, 0], If[Mod[37, 2] ≟ 1, (2 * π), π]) → B37
  47. CurveCartesian((abs((Element[Seq, 39] - Element[Seq, 38]) / 2) * cos(u)) + (Element[Seq, 39] + Element[Seq, 38]) / 2, (abs((Element[Seq, 39] - Element[Seq, 38]) / 2) * sin(u)), u, If[Mod[38, 2] ≟ 1, π, 0], If[Mod[38, 2] ≟ 1, (2 * π), π]) → B38
  48. CurveCartesian((abs((Element[Seq, 40] - Element[Seq, 39]) / 2) * cos(u)) + (Element[Seq, 40] + Element[Seq, 39]) / 2, (abs((Element[Seq, 40] - Element[Seq, 39]) / 2) * sin(u)), u, If[Mod[39, 2] ≟ 1, π, 0], If[Mod[39, 2] ≟ 1, (2 * π), π]) → B39
  49. CurveCartesian((abs((Element[Seq, 41] - Element[Seq, 40]) / 2) * cos(u)) + (Element[Seq, 41] + Element[Seq, 40]) / 2, (abs((Element[Seq, 41] - Element[Seq, 40]) / 2) * sin(u)), u, If[Mod[40, 2] ≟ 1, π, 0], If[Mod[40, 2] ≟ 1, (2 * π), π]) → B40
  50. CurveCartesian((abs((Element[Seq, 42] - Element[Seq, 41]) / 2) * cos(u)) + (Element[Seq, 42] + Element[Seq, 41]) / 2, (abs((Element[Seq, 42] - Element[Seq, 41]) / 2) * sin(u)), u, If[Mod[41, 2] ≟ 1, π, 0], If[Mod[41, 2] ≟ 1, (2 * π), π]) → B41
  51. CurveCartesian((abs((Element[Seq, 43] - Element[Seq, 42]) / 2) * cos(u)) + (Element[Seq, 43] + Element[Seq, 42]) / 2, (abs((Element[Seq, 43] - Element[Seq, 42]) / 2) * sin(u)), u, If[Mod[42, 2] ≟ 1, π, 0], If[Mod[42, 2] ≟ 1, (2 * π), π]) → B42
  52. CurveCartesian((abs((Element[Seq, 44] - Element[Seq, 43]) / 2) * cos(u)) + (Element[Seq, 44] + Element[Seq, 43]) / 2, (abs((Element[Seq, 44] - Element[Seq, 43]) / 2) * sin(u)), u, If[Mod[43, 2] ≟ 1, π, 0], If[Mod[43, 2] ≟ 1, (2 * π), π]) → B43
  53. CurveCartesian((abs((Element[Seq, 45] - Element[Seq, 44]) / 2) * cos(u)) + (Element[Seq, 45] + Element[Seq, 44]) / 2, (abs((Element[Seq, 45] - Element[Seq, 44]) / 2) * sin(u)), u, If[Mod[44, 2] ≟ 1, π, 0], If[Mod[44, 2] ≟ 1, (2 * π), π]) → B44
  54. CurveCartesian((abs((Element[Seq, 46] - Element[Seq, 45]) / 2) * cos(u)) + (Element[Seq, 46] + Element[Seq, 45]) / 2, (abs((Element[Seq, 46] - Element[Seq, 45]) / 2) * sin(u)), u, If[Mod[45, 2] ≟ 1, π, 0], If[Mod[45, 2] ≟ 1, (2 * π), π]) → B45
  55. CurveCartesian((abs((Element[Seq, 47] - Element[Seq, 46]) / 2) * cos(u)) + (Element[Seq, 47] + Element[Seq, 46]) / 2, (abs((Element[Seq, 47] - Element[Seq, 46]) / 2) * sin(u)), u, If[Mod[46, 2] ≟ 1, π, 0], If[Mod[46, 2] ≟ 1, (2 * π), π]) → B46
  56. CurveCartesian((abs((Element[Seq, 48] - Element[Seq, 47]) / 2) * cos(u)) + (Element[Seq, 48] + Element[Seq, 47]) / 2, (abs((Element[Seq, 48] - Element[Seq, 47]) / 2) * sin(u)), u, If[Mod[47, 2] ≟ 1, π, 0], If[Mod[47, 2] ≟ 1, (2 * π), π]) → B47
  57. CurveCartesian((abs((Element[Seq, 49] - Element[Seq, 48]) / 2) * cos(u)) + (Element[Seq, 49] + Element[Seq, 48]) / 2, (abs((Element[Seq, 49] - Element[Seq, 48]) / 2) * sin(u)), u, If[Mod[48, 2] ≟ 1, π, 0], If[Mod[48, 2] ≟ 1, (2 * π), π]) → B48
  58. CurveCartesian((abs((Element[Seq, 50] - Element[Seq, 49]) / 2) * cos(u)) + (Element[Seq, 50] + Element[Seq, 49]) / 2, (abs((Element[Seq, 50] - Element[Seq, 49]) / 2) * sin(u)), u, If[Mod[49, 2] ≟ 1, π, 0], If[Mod[49, 2] ≟ 1, (2 * π), π]) → B49
  59. CurveCartesian((abs((Element[Seq, 51] - Element[Seq, 50]) / 2) * cos(u)) + (Element[Seq, 51] + Element[Seq, 50]) / 2, (abs((Element[Seq, 51] - Element[Seq, 50]) / 2) * sin(u)), u, If[Mod[50, 2] ≟ 1, π, 0], If[Mod[50, 2] ≟ 1, (2 * π), π]) → B50
  60. CurveCartesian((abs((Element[Seq, 52] - Element[Seq, 51]) / 2) * cos(u)) + (Element[Seq, 52] + Element[Seq, 51]) / 2, (abs((Element[Seq, 52] - Element[Seq, 51]) / 2) * sin(u)), u, If[Mod[51, 2] ≟ 1, π, 0], If[Mod[51, 2] ≟ 1, (2 * π), π]) → B51
  61. CurveCartesian((abs((Element[Seq, 53] - Element[Seq, 52]) / 2) * cos(u)) + (Element[Seq, 53] + Element[Seq, 52]) / 2, (abs((Element[Seq, 53] - Element[Seq, 52]) / 2) * sin(u)), u, If[Mod[52, 2] ≟ 1, π, 0], If[Mod[52, 2] ≟ 1, (2 * π), π]) → B52
  62. CurveCartesian((abs((Element[Seq, 54] - Element[Seq, 53]) / 2) * cos(u)) + (Element[Seq, 54] + Element[Seq, 53]) / 2, (abs((Element[Seq, 54] - Element[Seq, 53]) / 2) * sin(u)), u, If[Mod[53, 2] ≟ 1, π, 0], If[Mod[53, 2] ≟ 1, (2 * π), π]) → B53
  63. CurveCartesian((abs((Element[Seq, 55] - Element[Seq, 54]) / 2) * cos(u)) + (Element[Seq, 55] + Element[Seq, 54]) / 2, (abs((Element[Seq, 55] - Element[Seq, 54]) / 2) * sin(u)), u, If[Mod[54, 2] ≟ 1, π, 0], If[Mod[54, 2] ≟ 1, (2 * π), π]) → B54
  64. CurveCartesian((abs((Element[Seq, 56] - Element[Seq, 55]) / 2) * cos(u)) + (Element[Seq, 56] + Element[Seq, 55]) / 2, (abs((Element[Seq, 56] - Element[Seq, 55]) / 2) * sin(u)), u, If[Mod[55, 2] ≟ 1, π, 0], If[Mod[55, 2] ≟ 1, (2 * π), π]) → B55
  65. CurveCartesian((abs((Element[Seq, 57] - Element[Seq, 56]) / 2) * cos(u)) + (Element[Seq, 57] + Element[Seq, 56]) / 2, (abs((Element[Seq, 57] - Element[Seq, 56]) / 2) * sin(u)), u, If[Mod[56, 2] ≟ 1, π, 0], If[Mod[56, 2] ≟ 1, (2 * π), π]) → B56
  66. CurveCartesian((abs((Element[Seq, 58] - Element[Seq, 57]) / 2) * cos(u)) + (Element[Seq, 58] + Element[Seq, 57]) / 2, (abs((Element[Seq, 58] - Element[Seq, 57]) / 2) * sin(u)), u, If[Mod[57, 2] ≟ 1, π, 0], If[Mod[57, 2] ≟ 1, (2 * π), π]) → B57
  67. CurveCartesian((abs((Element[Seq, 59] - Element[Seq, 58]) / 2) * cos(u)) + (Element[Seq, 59] + Element[Seq, 58]) / 2, (abs((Element[Seq, 59] - Element[Seq, 58]) / 2) * sin(u)), u, If[Mod[58, 2] ≟ 1, π, 0], If[Mod[58, 2] ≟ 1, (2 * π), π]) → B58
  68. CurveCartesian((abs((Element[Seq, 60] - Element[Seq, 59]) / 2) * cos(u)) + (Element[Seq, 60] + Element[Seq, 59]) / 2, (abs((Element[Seq, 60] - Element[Seq, 59]) / 2) * sin(u)), u, If[Mod[59, 2] ≟ 1, π, 0], If[Mod[59, 2] ≟ 1, (2 * π), π]) → B59
  69. CurveCartesian((abs((Element[Seq, 61] - Element[Seq, 60]) / 2) * cos(u)) + (Element[Seq, 61] + Element[Seq, 60]) / 2, (abs((Element[Seq, 61] - Element[Seq, 60]) / 2) * sin(u)), u, If[Mod[60, 2] ≟ 1, π, 0], If[Mod[60, 2] ≟ 1, (2 * π), π]) → B60
  70. CurveCartesian((abs((Element[Seq, 62] - Element[Seq, 61]) / 2) * cos(u)) + (Element[Seq, 62] + Element[Seq, 61]) / 2, (abs((Element[Seq, 62] - Element[Seq, 61]) / 2) * sin(u)), u, If[Mod[61, 2] ≟ 1, π, 0], If[Mod[61, 2] ≟ 1, (2 * π), π]) → B61
  71. CurveCartesian((abs((Element[Seq, 63] - Element[Seq, 62]) / 2) * cos(u)) + (Element[Seq, 63] + Element[Seq, 62]) / 2, (abs((Element[Seq, 63] - Element[Seq, 62]) / 2) * sin(u)), u, If[Mod[62, 2] ≟ 1, π, 0], If[Mod[62, 2] ≟ 1, (2 * π), π]) → B62
  72. CurveCartesian((abs((Element[Seq, 64] - Element[Seq, 63]) / 2) * cos(u)) + (Element[Seq, 64] + Element[Seq, 63]) / 2, (abs((Element[Seq, 64] - Element[Seq, 63]) / 2) * sin(u)), u, If[Mod[63, 2] ≟ 1, π, 0], If[Mod[63, 2] ≟ 1, (2 * π), π]) → B63
  73. CurveCartesian((abs((Element[Seq, 65] - Element[Seq, 64]) / 2) * cos(u)) + (Element[Seq, 65] + Element[Seq, 64]) / 2, (abs((Element[Seq, 65] - Element[Seq, 64]) / 2) * sin(u)), u, If[Mod[64, 2] ≟ 1, π, 0], If[Mod[64, 2] ≟ 1, (2 * π), π]) → B64
  74. CurveCartesian((abs((Element[Seq, 66] - Element[Seq, 65]) / 2) * cos(u)) + (Element[Seq, 66] + Element[Seq, 65]) / 2, (abs((Element[Seq, 66] - Element[Seq, 65]) / 2) * sin(u)), u, If[Mod[65, 2] ≟ 1, π, 0], If[Mod[65, 2] ≟ 1, (2 * π), π]) → B65
  75. CurveCartesian((abs((Element[Seq, 67] - Element[Seq, 66]) / 2) * cos(u)) + (Element[Seq, 67] + Element[Seq, 66]) / 2, (abs((Element[Seq, 67] - Element[Seq, 66]) / 2) * sin(u)), u, If[Mod[66, 2] ≟ 1, π, 0], If[Mod[66, 2] ≟ 1, (2 * π), π]) → B66
  76. CurveCartesian((abs((Element[Seq, 68] - Element[Seq, 67]) / 2) * cos(u)) + (Element[Seq, 68] + Element[Seq, 67]) / 2, (abs((Element[Seq, 68] - Element[Seq, 67]) / 2) * sin(u)), u, If[Mod[67, 2] ≟ 1, π, 0], If[Mod[67, 2] ≟ 1, (2 * π), π]) → B67
  77. CurveCartesian((abs((Element[Seq, 69] - Element[Seq, 68]) / 2) * cos(u)) + (Element[Seq, 69] + Element[Seq, 68]) / 2, (abs((Element[Seq, 69] - Element[Seq, 68]) / 2) * sin(u)), u, If[Mod[68, 2] ≟ 1, π, 0], If[Mod[68, 2] ≟ 1, (2 * π), π]) → B68
  78. CurveCartesian((abs((Element[Seq, 70] - Element[Seq, 69]) / 2) * cos(u)) + (Element[Seq, 70] + Element[Seq, 69]) / 2, (abs((Element[Seq, 70] - Element[Seq, 69]) / 2) * sin(u)), u, If[Mod[69, 2] ≟ 1, π, 0], If[Mod[69, 2] ≟ 1, (2 * π), π]) → B69
  79. CurveCartesian((abs((Element[Seq, 71] - Element[Seq, 70]) / 2) * cos(u)) + (Element[Seq, 71] + Element[Seq, 70]) / 2, (abs((Element[Seq, 71] - Element[Seq, 70]) / 2) * sin(u)), u, If[Mod[70, 2] ≟ 1, π, 0], If[Mod[70, 2] ≟ 1, (2 * π), π]) → B70
  80. CurveCartesian((abs((Element[Seq, 72] - Element[Seq, 71]) / 2) * cos(u)) + (Element[Seq, 72] + Element[Seq, 71]) / 2, (abs((Element[Seq, 72] - Element[Seq, 71]) / 2) * sin(u)), u, If[Mod[71, 2] ≟ 1, π, 0], If[Mod[71, 2] ≟ 1, (2 * π), π]) → B71
  81. CurveCartesian((abs((Element[Seq, 73] - Element[Seq, 72]) / 2) * cos(u)) + (Element[Seq, 73] + Element[Seq, 72]) / 2, (abs((Element[Seq, 73] - Element[Seq, 72]) / 2) * sin(u)), u, If[Mod[72, 2] ≟ 1, π, 0], If[Mod[72, 2] ≟ 1, (2 * π), π]) → B72
  82. CurveCartesian((abs((Element[Seq, 74] - Element[Seq, 73]) / 2) * cos(u)) + (Element[Seq, 74] + Element[Seq, 73]) / 2, (abs((Element[Seq, 74] - Element[Seq, 73]) / 2) * sin(u)), u, If[Mod[73, 2] ≟ 1, π, 0], If[Mod[73, 2] ≟ 1, (2 * π), π]) → B73
  83. CurveCartesian((abs((Element[Seq, 75] - Element[Seq, 74]) / 2) * cos(u)) + (Element[Seq, 75] + Element[Seq, 74]) / 2, (abs((Element[Seq, 75] - Element[Seq, 74]) / 2) * sin(u)), u, If[Mod[74, 2] ≟ 1, π, 0], If[Mod[74, 2] ≟ 1, (2 * π), π]) → B74
  84. CurveCartesian((abs((Element[Seq, 76] - Element[Seq, 75]) / 2) * cos(u)) + (Element[Seq, 76] + Element[Seq, 75]) / 2, (abs((Element[Seq, 76] - Element[Seq, 75]) / 2) * sin(u)), u, If[Mod[75, 2] ≟ 1, π, 0], If[Mod[75, 2] ≟ 1, (2 * π), π]) → B75
  85. CurveCartesian((abs((Element[Seq, 77] - Element[Seq, 76]) / 2) * cos(u)) + (Element[Seq, 77] + Element[Seq, 76]) / 2, (abs((Element[Seq, 77] - Element[Seq, 76]) / 2) * sin(u)), u, If[Mod[76, 2] ≟ 1, π, 0], If[Mod[76, 2] ≟ 1, (2 * π), π]) → B76
  86. CurveCartesian((abs((Element[Seq, 78] - Element[Seq, 77]) / 2) * cos(u)) + (Element[Seq, 78] + Element[Seq, 77]) / 2, (abs((Element[Seq, 78] - Element[Seq, 77]) / 2) * sin(u)), u, If[Mod[77, 2] ≟ 1, π, 0], If[Mod[77, 2] ≟ 1, (2 * π), π]) → B77
  87. CurveCartesian((abs((Element[Seq, 79] - Element[Seq, 78]) / 2) * cos(u)) + (Element[Seq, 79] + Element[Seq, 78]) / 2, (abs((Element[Seq, 79] - Element[Seq, 78]) / 2) * sin(u)), u, If[Mod[78, 2] ≟ 1, π, 0], If[Mod[78, 2] ≟ 1, (2 * π), π]) → B78
  88. CurveCartesian((abs((Element[Seq, 80] - Element[Seq, 79]) / 2) * cos(u)) + (Element[Seq, 80] + Element[Seq, 79]) / 2, (abs((Element[Seq, 80] - Element[Seq, 79]) / 2) * sin(u)), u, If[Mod[79, 2] ≟ 1, π, 0], If[Mod[79, 2] ≟ 1, (2 * π), π]) → B79
  89. CurveCartesian((abs((Element[Seq, 81] - Element[Seq, 80]) / 2) * cos(u)) + (Element[Seq, 81] + Element[Seq, 80]) / 2, (abs((Element[Seq, 81] - Element[Seq, 80]) / 2) * sin(u)), u, If[Mod[80, 2] ≟ 1, π, 0], If[Mod[80, 2] ≟ 1, (2 * π), π]) → B80
  90. CurveCartesian((abs((Element[Seq, 82] - Element[Seq, 81]) / 2) * cos(u)) + (Element[Seq, 82] + Element[Seq, 81]) / 2, (abs((Element[Seq, 82] - Element[Seq, 81]) / 2) * sin(u)), u, If[Mod[81, 2] ≟ 1, π, 0], If[Mod[81, 2] ≟ 1, (2 * π), π]) → B81
  91. CurveCartesian((abs((Element[Seq, 83] - Element[Seq, 82]) / 2) * cos(u)) + (Element[Seq, 83] + Element[Seq, 82]) / 2, (abs((Element[Seq, 83] - Element[Seq, 82]) / 2) * sin(u)), u, If[Mod[82, 2] ≟ 1, π, 0], If[Mod[82, 2] ≟ 1, (2 * π), π]) → B82
  92. CurveCartesian((abs((Element[Seq, 84] - Element[Seq, 83]) / 2) * cos(u)) + (Element[Seq, 84] + Element[Seq, 83]) / 2, (abs((Element[Seq, 84] - Element[Seq, 83]) / 2) * sin(u)), u, If[Mod[83, 2] ≟ 1, π, 0], If[Mod[83, 2] ≟ 1, (2 * π), π]) → B83
  93. CurveCartesian((abs((Element[Seq, 85] - Element[Seq, 84]) / 2) * cos(u)) + (Element[Seq, 85] + Element[Seq, 84]) / 2, (abs((Element[Seq, 85] - Element[Seq, 84]) / 2) * sin(u)), u, If[Mod[84, 2] ≟ 1, π, 0], If[Mod[84, 2] ≟ 1, (2 * π), π]) → B84
  94. CurveCartesian((abs((Element[Seq, 86] - Element[Seq, 85]) / 2) * cos(u)) + (Element[Seq, 86] + Element[Seq, 85]) / 2, (abs((Element[Seq, 86] - Element[Seq, 85]) / 2) * sin(u)), u, If[Mod[85, 2] ≟ 1, π, 0], If[Mod[85, 2] ≟ 1, (2 * π), π]) → B85
  95. CurveCartesian((abs((Element[Seq, 87] - Element[Seq, 86]) / 2) * cos(u)) + (Element[Seq, 87] + Element[Seq, 86]) / 2, (abs((Element[Seq, 87] - Element[Seq, 86]) / 2) * sin(u)), u, If[Mod[86, 2] ≟ 1, π, 0], If[Mod[86, 2] ≟ 1, (2 * π), π]) → B86
  96. CurveCartesian((abs((Element[Seq, 88] - Element[Seq, 87]) / 2) * cos(u)) + (Element[Seq, 88] + Element[Seq, 87]) / 2, (abs((Element[Seq, 88] - Element[Seq, 87]) / 2) * sin(u)), u, If[Mod[87, 2] ≟ 1, π, 0], If[Mod[87, 2] ≟ 1, (2 * π), π]) → B87
  97. CurveCartesian((abs((Element[Seq, 89] - Element[Seq, 88]) / 2) * cos(u)) + (Element[Seq, 89] + Element[Seq, 88]) / 2, (abs((Element[Seq, 89] - Element[Seq, 88]) / 2) * sin(u)), u, If[Mod[88, 2] ≟ 1, π, 0], If[Mod[88, 2] ≟ 1, (2 * π), π]) → B88
  98. CurveCartesian((abs((Element[Seq, 90] - Element[Seq, 89]) / 2) * cos(u)) + (Element[Seq, 90] + Element[Seq, 89]) / 2, (abs((Element[Seq, 90] - Element[Seq, 89]) / 2) * sin(u)), u, If[Mod[89, 2] ≟ 1, π, 0], If[Mod[89, 2] ≟ 1, (2 * π), π]) → B89
  99. CurveCartesian((abs((Element[Seq, 91] - Element[Seq, 90]) / 2) * cos(u)) + (Element[Seq, 91] + Element[Seq, 90]) / 2, (abs((Element[Seq, 91] - Element[Seq, 90]) / 2) * sin(u)), u, If[Mod[90, 2] ≟ 1, π, 0], If[Mod[90, 2] ≟ 1, (2 * π), π]) → B90
  100. CurveCartesian((abs((Element[Seq, 92] - Element[Seq, 91]) / 2) * cos(u)) + (Element[Seq, 92] + Element[Seq, 91]) / 2, (abs((Element[Seq, 92] - Element[Seq, 91]) / 2) * sin(u)), u, If[Mod[91, 2] ≟ 1, π, 0], If[Mod[91, 2] ≟ 1, (2 * π), π]) → B91
  101. CurveCartesian((abs((Element[Seq, 93] - Element[Seq, 92]) / 2) * cos(u)) + (Element[Seq, 93] + Element[Seq, 92]) / 2, (abs((Element[Seq, 93] - Element[Seq, 92]) / 2) * sin(u)), u, If[Mod[92, 2] ≟ 1, π, 0], If[Mod[92, 2] ≟ 1, (2 * π), π]) → B92
  102. CurveCartesian((abs((Element[Seq, 94] - Element[Seq, 93]) / 2) * cos(u)) + (Element[Seq, 94] + Element[Seq, 93]) / 2, (abs((Element[Seq, 94] - Element[Seq, 93]) / 2) * sin(u)), u, If[Mod[93, 2] ≟ 1, π, 0], If[Mod[93, 2] ≟ 1, (2 * π), π]) → B93
  103. CurveCartesian((abs((Element[Seq, 95] - Element[Seq, 94]) / 2) * cos(u)) + (Element[Seq, 95] + Element[Seq, 94]) / 2, (abs((Element[Seq, 95] - Element[Seq, 94]) / 2) * sin(u)), u, If[Mod[94, 2] ≟ 1, π, 0], If[Mod[94, 2] ≟ 1, (2 * π), π]) → B94
  104. CurveCartesian((abs((Element[Seq, 96] - Element[Seq, 95]) / 2) * cos(u)) + (Element[Seq, 96] + Element[Seq, 95]) / 2, (abs((Element[Seq, 96] - Element[Seq, 95]) / 2) * sin(u)), u, If[Mod[95, 2] ≟ 1, π, 0], If[Mod[95, 2] ≟ 1, (2 * π), π]) → B95
  105. CurveCartesian((abs((Element[Seq, 97] - Element[Seq, 96]) / 2) * cos(u)) + (Element[Seq, 97] + Element[Seq, 96]) / 2, (abs((Element[Seq, 97] - Element[Seq, 96]) / 2) * sin(u)), u, If[Mod[96, 2] ≟ 1, π, 0], If[Mod[96, 2] ≟ 1, (2 * π), π]) → B96
  106. CurveCartesian((abs((Element[Seq, 98] - Element[Seq, 97]) / 2) * cos(u)) + (Element[Seq, 98] + Element[Seq, 97]) / 2, (abs((Element[Seq, 98] - Element[Seq, 97]) / 2) * sin(u)), u, If[Mod[97, 2] ≟ 1, π, 0], If[Mod[97, 2] ≟ 1, (2 * π), π]) → B97
  107. CurveCartesian((abs((Element[Seq, 99] - Element[Seq, 98]) / 2) * cos(u)) + (Element[Seq, 99] + Element[Seq, 98]) / 2, (abs((Element[Seq, 99] - Element[Seq, 98]) / 2) * sin(u)), u, If[Mod[98, 2] ≟ 1, π, 0], If[Mod[98, 2] ≟ 1, (2 * π), π]) → B98
  108. CurveCartesian((abs((Element[Seq, 100] - Element[Seq, 99]) / 2) * cos(u)) + (Element[Seq, 100] + Element[Seq, 99]) / 2, (abs((Element[Seq, 100] - Element[Seq, 99]) / 2) * sin(u)), u, If[Mod[99, 2] ≟ 1, π, 0], If[Mod[99, 2] ≟ 1, (2 * π), π]) → B99
  109. CurveCartesian((abs((Element[Seq, 101] - Element[Seq, 100]) / 2) * cos(u)) + (Element[Seq, 101] + Element[Seq, 100]) / 2, (abs((Element[Seq, 101] - Element[Seq, 100]) / 2) * sin(u)), u, If[Mod[100, 2] ≟ 1, π, 0], If[Mod[100, 2] ≟ 1, (2 * π), π]) → B100
  110. If(n ≤ 4, 6, Max[Element[Seq, n], Element[Seq, n + 1]]) → lastVal