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Butterfly Effect in Fraction Addition

Butterfly Effect in Fraction Addition
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2020-04-01 17:58
Matrix
This example dynamically visualizes the significant impact of minor variations in fraction addition, mirroring the butterfly effect phenomenon. It involves core mathematical concepts such as fraction operations, matrix transformations, geometric constructions, and continuity. GeoGebra commands and objects like Random, If, Ellipse, OrthogonalLine, Mirror, Point, CircumcircleArc, Segment, GCD, and Vector are used to construct the visualization. It is suitable for high school mathematics education, helping students explore the connection between chaos theory and fraction operations, and inspiring them to investigate complex dynamic systems in mathematics.

GeoGebra Commands & Parameters

  1. Random(1, 9) → n'1
  2. Random(1, 9) → d1
  3. Random(1, 9) → d'2
  4. If(n'1 ≟ d1, n'1 + 1, n'1) → n1
  5. Random(1, 9) → n2
  6. If(d'2 ≟ d1, d1 + 1, d'2) → d2
  7. Ellipse(A, B, C) → c
  8. OrthogonalLine(D, xAxis) → a
  9. Mirror(c, a) → c'
  10. Point(c) → E
  11. CircumcircleArc(E, F, G) → d
  12. CircumcircleArc(G, H, I) → e
  13. Mirror(E, a) → E'
  14. Mirror(F, a) → F'
  15. Mirror(G, a) → G'
  16. CircumcircleArc(E', F', G') → d'
  17. Mirror(G, a) → G'_1
  18. Mirror(H, a) → H'
  19. Mirror(I, a) → I'
  20. CircumcircleArc(G'_1, H', I') → e'
  21. Segment(J, K) → b
  22. Mirror(J, a) → J'
  23. Mirror(K, a) → K'
  24. Segment(J', K') → b'
  25. Point(c') → L
  26. Point(a) → M
  27. CircumcircleArc(L, O, M) → f
  28. Mirror(L, a) → L'
  29. Mirror(O, a) → O'
  30. Mirror(M, a) → M'
  31. CircumcircleArc(L', O', M') → f'
  32. Segment(N, P) → g
  33. GCD(nres, dd) → m
  34. Segment(Q, R) → h
  35. CircumcircleArc(S, T, U) → k
  36. CircumcircleArc(V, W, Z) → p
  37. Point(k) → A_1
  38. Vector(A_1, U) → u
  39. Point(p) → B_1
  40. Vector(B_1, Z) → v