Lissajous Curve Generator by Mark Kaercher
Loading the math board and drawing, please wait…
This example demonstrates the generation of Lissajous curves, which are parametric equations of sine or cosine functions. Lissajous curves are often used to study vibrations and waveforms. By adjusting parameters a, b, and c, various shapes of Lissajous curves can be observed. The CurveCartesian command is used to draw the curves. Suitable for high school mathematics education, particularly in coordinate geometry and trigonometry.
GeoGebra Commands & Parameters
CurveCartesian((cos((a * t)), sin((b * t))), t, 0, (2 * 3.141592653589793)) → c
AI Drawing Prompt Reference
Draw a Lissajous curve defined by parametric equations where the x-coordinate is a cosine function and the y-coordinate is a sine function, with the parameter ranging from zero to two pi. Adjust three parameters to vary the curve's shape, producing different closed or open patterns. The curve should be smooth and continuous, illustrating the typical form of superimposed vibrations, suitable for high school trigonometry and coordinate geometry demonstration.
The prompt above was compiled from the original drawing commands and is for reference only.