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Lissajous Figure Intersection Demo

Lissajous Figure Intersection Demo
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2024-02-15 03:24
TrigonometryCoordinate GeometryParametric EquationGraphing
In collections intersection: surface-surface, curve-curve
This example demonstrates the intersection points of two Lissajous figures. Key math concepts include parametric equations, trigonometric functions, and coordinate geometry. It is constructed using GeoGebra commands like Textfield, CurveCartesian, and LaTeX, with objects such as n_2, n_1, t_{b1}, and sliders for interactive exploration. Suitable for high school and above to understand parametric equations and function graph intersections.

GeoGebra Commands & Parameters

  1. Textfield(h) → InputBox1
  2. CurveCartesian((5 * sin((n_1 * t))), (10 * sin((n_2 * t))), t, 0, t_{b1}) → b1
  3. CurveCartesian((7 * sin((2 * t))) + x(A), (10 * sin((5 * t))) + y(A), t, 0, t_{a1}) → a1
  4. LaTeX(a1, false, false) → text4a
  5. LaTeX(b1, false, false) → text4b
  6. Textfield(a1) → InputBox2
  7. Textfield(b1) → InputBox3
  8. Textfield(n_1) → InputBox4
  9. Textfield(n_2) → InputBox5
  10. Textfield(f) → InputBox6
  11. Textfield(t_{a1}) → InputBox7
  12. Textfield(t_{b1}) → InputBox8

AI Drawing Prompt Reference

Draw the intersection points of two Lissajous curves. The first curve is defined by parametric equations x=5*sin(n1*t) and y=10*sin(n2*t). The second curve is defined by x=7*sin(2*t)+x0 and y=10*sin(5*t)+y0. The intersection points depend on parameters n1, n2, and time t. Adjust these parameters to observe changes in intersection points. The graph should clearly show the intersection points and their surrounding areas.
The prompt above was compiled from the original drawing commands and is for reference only.