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Square Wave

Square Wave
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2015-08-15 05:48
TrigonometrySequenceGraphing
This example demonstrates the generation of a square wave. Key mathematical concepts include trigonometry and sequences. Using GeoGebra commands such as Circle, Intersect, Rotate, and Sequence, the formation of the square wave is dynamically shown. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle(A, 1.2732395447351628) → c
  2. Intersect(c, xAxis, 2) → B
  3. Rotate(B, t, A) → B'
  4. Circle(B', 0.4244131815783876) → d
  5. Line(B', xAxis) → a
  6. Intersect(d, a, 2) → C
  7. Rotate(C, (3 * t), B') → C'
  8. Circle(C', 0.25464790894703254) → e
  9. Line(C', a) → b
  10. Intersect(e, b, 2) → D
  11. Rotate(D, (5 * t), C') → D'
  12. Circle(D', 0.18189136353359467) → f
  13. Line(D', b) → g
  14. Intersect(f, g, 2) → E
  15. Rotate(E, (7 * t), D') → E'
  16. Circle(E', 0.1414710605261292) → h
  17. Line(E', g) → i
  18. Intersect(h, i, 2) → F
  19. Rotate(F, (9 * t), E') → F'
  20. Segment(F', E') → j
  21. Segment(E', D') → k
  22. Segment(D', C') → l
  23. Segment(C', B') → m
  24. Segment(B', A) → n
  25. CurveCartesian(s, Sum[Sequence[(4 / ((π * n)) * sin((n * s))), n, 1, 9, 2]], s, 0, t) → o
  26. Locus(G, t) → loc1
  27. Sequence(If[0 ≤ x ≤ 6.28319, (4 / ((π * n)) * sin((n * x)))], n, 1, w, 2) → list1
  28. Sum(list1) → p
  29. PolyLine((0, -1), (0, 1), (3.141592653589793, 1), (3.141592653589793, -1), (6.28319, -1), (6.28319, 1)) → q
  30. Segment(F', G) → r
  31. Segment((0, 2), (0, -2)) → c_1