# Lissajous-Figur -- 2020 -- 7766

- By: Dietmar Rabich
- Date: Taken on 8 June 2020, 17:33
- Classification: Photograph
- Museum: [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Lissajous-Figur_--_2020_--_7766.jpg)
- Rights: [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0)
- Picture: https://invisiblenetwork.ai/thumbs/commons/thumb/8/83/Lissajous-Figur_--_2020_--_7766.jpg/1920px-Lissajous-Figur_--_2020_--_7766.jpg
- Who can see it: Kids profiles and older (museums give no ratings; placed by Invisible Network from the museum's own words)

Traces of light based on Lissajous figures Lissajous figures are characteristic curves that arise when two harmonic oscillations overlap—usually at right angles to each other. They were studied in the 19th century by French physicist Jules Antoine Lissajous. Mathematically, they are created by two sine or cosine functions with possibly different frequencies and phase shifts. If the frequencies are the same, the result is a straight line, a circle, or an ellipse, depending on the phase. Different frequency ratios produce complex, closed loop patterns. Lissajous figures can be seen on an oscilloscope, for example, when two alternating voltages are applied to the X and Y deflection. The shape of the figure provides information about the frequency ratio and phase position of the signals. They play a role in physics, technology, and acoustics and combine mathematical precision with aesthetic diversity of form.