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Spirographic Curves 2

Spirographic Curves 2
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2020-02-04 00:01
FunctionTrigonometryCalculusParametric EquationGraphing
This example demonstrates the generation of complex spirographic curves through controlled rotation parameters, involving function graphs, integral calculus, parabolas, prisms, and cones. Key GeoGebra commands like Sequence, Join, and Element are used to construct the curves, leveraging parameters n, v, l1, A1-A36 for dynamic control. Suitable for high school and above, exploring parametric equations, locus formation, and geometric transformations in function graphing.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[CurveCartesian[sin((i * t)) + sin(((sgn(i - j) * j) * t)) + sin((n * t)) + (6.5 * i), cos((i * t)) + cos(((sgn(i - j) * j) * t)) + cos((n * t)) + (6.5 * j), t, 0, v], i, 1, 8], j, 1, 5) → l1
  2. Join(l1) → l2
  3. Element(l2, A1) → B1
  4. Element(l2, A2) → B2
  5. Element(l2, A3) → B3
  6. Element(l2, A4) → B4
  7. Element(l2, A5) → B5
  8. Element(l2, A6) → B6
  9. Element(l2, A7) → B7
  10. Element(l2, A8) → B8
  11. Element(l2, A9) → B9
  12. Element(l2, A10) → B10
  13. Element(l2, A11) → B11
  14. Element(l2, A12) → B12
  15. Element(l2, A13) → B13
  16. Element(l2, A14) → B14
  17. Element(l2, A15) → B15
  18. Element(l2, A16) → B16
  19. Element(l2, A17) → B17
  20. Element(l2, A18) → B18
  21. Element(l2, A19) → B19
  22. Element(l2, A20) → B20
  23. Element(l2, A21) → B21
  24. Element(l2, A22) → B22
  25. Element(l2, A23) → B23
  26. Element(l2, A24) → B24
  27. Element(l2, A25) → B25
  28. Element(l2, A26) → B26
  29. Element(l2, A27) → B27
  30. Element(l2, A28) → B28
  31. Element(l2, A29) → B29
  32. Element(l2, A30) → B30
  33. Element(l2, A31) → B31
  34. Element(l2, A32) → B32
  35. Element(l2, A33) → B33
  36. Element(l2, A34) → B34
  37. Element(l2, A35) → B35
  38. Element(l2, A36) → B36
  39. Element(l2, A37) → B37
  40. Element(l2, A38) → B38
  41. Element(l2, A39) → B39
  42. Element(l2, A40) → B40
  43. Element(l2, A41) → B41
  44. Element(l2, A42) → B42
  45. Element(l2, A43) → B43
  46. Element(l2, A44) → B44
  47. Element(l2, A45) → B45
  48. Element(l2, A46) → B46
  49. Element(l2, A47) → B47
  50. Element(l2, A48) → B48
  51. Element(l2, A49) → B49
  52. Sequence(Sequence[(sin((i * v)) + sin(((sgn(i - j) * j) * v)) + sin((n * v)) + (6.5 * i), cos((i * v)) + cos(((sgn(i - j) * j) * v)) + cos((n * v)) + (6.5 * j)), i, 1, 8], j, 1, 5) → l3