writer
6,694
edits
Changes
Jump to navigation
Jump to search
Manuals/calci/LISSAJOUSCURVE (view source)
Revision as of 22:32, 22 August 2017
, 22:32, 22 August 2017Created page with "<div style="font-size:30px">'''LISSAJOUSCURVE()'''</div><br/> ==Description== *This function shows the Lissajous curve for each values. *Lissajous Curve is a parametric plo..."
<div style="font-size:30px">'''LISSAJOUSCURVE()'''</div><br/>
==Description==
*This function shows the Lissajous curve for each values.
*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:The appearance of a figure is highly sensitive to a/b, the ratio of a and b.
*According to the ratio value, the shapes of the figures change in interesting ways.
*For a a/b ratio=1, the figure is an ellipse.
*For a=b, <math>\delta</math> = <math>\frac{\pi}{2}</math> radians, the figure is a circle.
*For <math>\delta</math> = 0, the figure is a line.
*For a/b = 2, <math>\delta</math> = <math>\frac{\pi}{4}</math>, the result is a 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/LISSAJOUS| LISSAJOUS ]]
==References==
*[https://en.wikibooks.org/wiki/Trigonometry/For_Enthusiasts/Lissajous_Figures Lissajous]
*[[Z_API_Functions | List of Main Z Functions]]
*[[ Z3 | Z3 home ]]
==Description==
*This function shows the Lissajous curve for each values.
*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:The appearance of a figure is highly sensitive to a/b, the ratio of a and b.
*According to the ratio value, the shapes of the figures change in interesting ways.
*For a a/b ratio=1, the figure is an ellipse.
*For a=b, <math>\delta</math> = <math>\frac{\pi}{2}</math> radians, the figure is a circle.
*For <math>\delta</math> = 0, the figure is a line.
*For a/b = 2, <math>\delta</math> = <math>\frac{\pi}{4}</math>, the result is a 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/LISSAJOUS| LISSAJOUS ]]
==References==
*[https://en.wikibooks.org/wiki/Trigonometry/For_Enthusiasts/Lissajous_Figures Lissajous]
*[[Z_API_Functions | List of Main Z Functions]]
*[[ Z3 | Z3 home ]]