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Created page with "<div style="font-size:30px">'''LISSAJOUS (TypeOrSettings,AsTable)'''</div><br/> *<math>TypeOrSettings</math> is any type like Ellipse or circle and so on. ==Description== *Th..."
<div style="font-size:30px">'''LISSAJOUS (TypeOrSettings,AsTable)'''</div><br/>
*<math>TypeOrSettings</math> is any type like Ellipse or circle and so on.
==Description==
*This function shows the values of the Lissajous curve.
*Lissajous Curve is a parametric plot of the harmonic system.
*It is also called Bowditch Curves.
*Lissajous used sounds of different frequencies to vibrate a mirror.
*A beam of light reflected from the mirror, was allowed to trace patterns which depended on the frequencies of the sounds – in a setup similar to projectors used in today's laser light shows.Lissajous figure is the intersection of two sinusoidal curves, the axes of which are at right angles to each other.
*Mathematically, this translates to a Complex harmonic function: In the Lissajous equation,a=1,b=1,A=1,B=1 and <math>\delta</math> = <math>\frac{\pi}{2}</math> radians, the figure is a circle.
*So these values substitute in the equation and it will shows the result.With the above values when <math>\delta</math>=0,then the value will show for line.
*In the same way the ratio <math>\frac{a}{b}</math>=1 and <math>\delta</math>=0,then the values will be shown for ellipse.
*Suppose <math>\frac{a}{b}</math> = 2, <math>\delta</math> = <math>\frac{\pi}{4}</math>, then the values will show for parabola.
*The Lissajous curve gets more complicated for other ratios, which are closed only if a/b is rational.
==Examples==
==See Also==
*[[Manuals/calci/FRACTAL | FRACTAL ]]
*[[Manuals/calci/LISSAJOUSCURVE| LISSAJOUSCURVE ]]
==References==
*[https://en.wikibooks.org/wiki/Trigonometry/For_Enthusiasts/Lissajous_Figures Lissajous]
*[[Z_API_Functions | List of Main Z Functions]]
*[[ Z3 | Z3 home ]]
*<math>TypeOrSettings</math> is any type like Ellipse or circle and so on.
==Description==
*This function shows the values of the Lissajous curve.
*Lissajous Curve is a parametric plot of the harmonic system.
*It is also called Bowditch Curves.
*Lissajous used sounds of different frequencies to vibrate a mirror.
*A beam of light reflected from the mirror, was allowed to trace patterns which depended on the frequencies of the sounds – in a setup similar to projectors used in today's laser light shows.Lissajous figure is the intersection of two sinusoidal curves, the axes of which are at right angles to each other.
*Mathematically, this translates to a Complex harmonic function: In the Lissajous equation,a=1,b=1,A=1,B=1 and <math>\delta</math> = <math>\frac{\pi}{2}</math> radians, the figure is a circle.
*So these values substitute in the equation and it will shows the result.With the above values when <math>\delta</math>=0,then the value will show for line.
*In the same way the ratio <math>\frac{a}{b}</math>=1 and <math>\delta</math>=0,then the values will be shown for ellipse.
*Suppose <math>\frac{a}{b}</math> = 2, <math>\delta</math> = <math>\frac{\pi}{4}</math>, then the values will show for parabola.
*The Lissajous curve gets more complicated for other ratios, which are closed only if a/b is rational.
==Examples==
==See Also==
*[[Manuals/calci/FRACTAL | FRACTAL ]]
*[[Manuals/calci/LISSAJOUSCURVE| LISSAJOUSCURVE ]]
==References==
*[https://en.wikibooks.org/wiki/Trigonometry/For_Enthusiasts/Lissajous_Figures Lissajous]
*[[Z_API_Functions | List of Main Z Functions]]
*[[ Z3 | Z3 home ]]