Lissajous Curves
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Curves and Surfaces
This example demonstrates Lissajous Curves, complex figures formed by the combination of two perpendicular simple harmonic vibrations. Core math concepts include parametric equations, trigonometric functions, coordinate geometry, and integral calculus. Constructed using GeoGebra's Curve command with parameters a, n, b, it is suitable for high school and above students to explore the properties and applications of parametric curves.
GeoGebra Commands & Parameters
CurveCartesian(cos(t), sin((a * t)), t, 0, (n * π)) → b
AI Drawing Prompt Reference
Draw a Lissajous curve in the coordinate plane as a parametric graph. Use parameter t to define x = cos(t) and y = sin(a·t), where the parameter a controls the vertical vibration frequency. Let t vary from 0 to n·π so the curve traces the resulting closed or intricate pattern. Render the parametric curve for that full t interval, with the shape determined by the frequency ratio implied by a and n.
The prompt above was compiled from the original drawing commands and is for reference only.