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Lissajous Divisibility

Lissajous Divisibility
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2019-03-19 12:40
VectorFunctionTrigonometrySequenceCoordinate Geometry
This example demonstrates the divisibility property of Lissajous curves under specific parameter conditions. It involves core math concepts like trigonometric functions, periodicity, divisibility, LCM, and GCD. Construction uses commands such as Sequence, Point, Ray, Vector, and objects like domain, l1, l2. Suitable for high school and above learners exploring parametric equations and coordinate geometry applications.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[CurveCartesian[cos((k * t)) + (2 * k), sin((j * t)) + (2 * j), t, Max[domain - 0.7 / k, 0], domain], k, j, 20], j, 1, 20) → l1
  2. Sequence(Sequence[CurveCartesian[cos((k * t)) + (2 * k), sin((j * t)) + (2 * j), t, 0, domain], k, j, 20], j, 1, 20) → l2
  3. Sequence(Sequence[((2 * k), (2 * j)), k, j, 20], j, 1, 20) → l3
  4. Point(l3) → B
  5. Ray(A, B) → f
  6. Vector(A, B) → u
  7. Vector((-1, -1)) → v
  8. Vector((1, -1)) → w
  9. Sequence(B + (k * u), k, 1, 20) → l4
  10. Sequence(Polygon[Element[l4, k] + v, Element[l4, k] + w, 4], k, 1, a) → l5

AI Drawing Prompt Reference

Draw a series of Lissajous curves with parameters k and j ranging from 1 to 20, which demonstrate divisibility under specific parameter conditions. First, draw Lissajous curves for each combination of k and j, then create a point set, followed by rays and vectors based on these points, and finally draw a series of quadrilaterals using these vectors as bases.
The prompt above was compiled from the original drawing commands and is for reference only.