Harmonograph (Equations)
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This example demonstrates the generation of complex Lissajous-like curves using parametric equations, where parameters like frequency, amplitude, phase shift, and damping are manipulated. It involves core mathematical concepts including trigonometric functions, parametric equations, and matrix operations. The construction uses the GeoGebra command CurveCartesian with sliders to control these parameters dynamically. Suitable for high school and above, it illustrates the application of parametric equations in graphing and the effect of parameter changes on curve shapes.
GeoGebra Commands & Parameters
CurveCartesian(X_t(t), Y_t(t), t, 0, time) → aCurveCartesian(X_1(t), Y_1(t), t, 0, time) → bCurveCartesian(X_2(t), Y_2(t), t, 0, time) → cCurveCartesian(X_t(t) + 0.05, Y_t(t) + 0.05, t, 0, time) → d
AI Drawing Prompt Reference
Draw complex Lissajous-like curves generated by parametric equations using sine and cosine functions, with sliders controlling frequency, amplitude, phase shift, and damping to show the effect of parameter changes on the curve shapes, slightly offset from the origin for emphasis.
The prompt above was compiled from the original drawing commands and is for reference only.