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Lissajous curve

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A Lissajous curve, also known as Lissajous figure or Bowditch curve, is the graph of a system of parametric equations

A Lissajous figure, made by releasing sand from a container at the end of a Blackburn pendulum

Lissajous figure on an oscilloscope, displaying a 1:3 relationship between the frequencies of the vertical and horizontal sinusoidal inputs, respectively. This particular Lissajous figure was adapted into the logo for the Australian Broadcasting Corporation

Parametric equation

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In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface, called a parametric curve and parametric surface, respectively. In such cases, the equations are collectively called a parametric representation, or parametric system, or parameterization of the object.

R = 6 r = 4 d = 1

R = 7 r = 4 d = 1

R = 8 r = 3 d = 2

R = 7 r = 4 d = 2