Скачать или смотреть Lissajous curves are graceful patterns formed by combining two perpendiịcular Oscillations,

Lissajous curves are graceful patternsformed by combining two perpendiịcularOscillations, typically one horizontal and onevertical, each varying sinusoidally in time.The exact shape depends on the ratio oftheir frequencies and the phase differencebetween them. When the frequenciesequal, the curve may appear as a straightline, an ellipse, ora circle. When thefrequencies differ, the path becomes moreintricate, producing looping, woven figuresthat repeat periodically when the ratio isrational. These curves provide a geometric
way to visualize how simple periodic motionsinteract. ]JOUS Mlachihe

Historically, Lissajous curves becameimportant through their use in oscilloscopes,where they helped engineers compare signalfrequencies and phase relationships. Beyondphysics and engineering, they appearnaturally in mathematics as parametricCurves and serve as beautiful examples ofhow complexity can arise from simple rules.Today, they are widely used in animation and visualization because small changes inparameters leàd to dramatič Viśual variation,making them ideal for illustrating ideas aboutharmony, resonance, and periodic motion ina visually intuitive way.


#math #beautiful #animation #physics