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- Lissajous_curve abstract "In mathematics, a Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous figure or Bowditch curve /ˈbaʊdɪtʃ/, is the graph of a system of parametric equations which describe complex harmonic motion. This family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissajous in 1857.The appearance of the figure is highly sensitive to the ratio a/b. For a ratio of 1, the figure is an ellipse, with special cases including circles (A = B, δ = π/2 radians) and lines (δ = 0). Another simple Lissajous figure is the parabola (a/b = 2, δ = π/4). Other ratios produce more complicated curves, which are closed only if a/b is rational. The visual form of these curves is often suggestive of a three-dimensional knot, and indeed many kinds of knots, including those known as Lissajous knots, project to the plane as Lissajous figures.Visually, the ratio a/b determines the number of "lobes" of the figure. For example, a ratio of 3/1 or 1/3 produces a figure with three major lobes (see image). Similarly, a ratio of 5/4 produces a figure with 5 horizontal lobes and 4 vertical lobes. Rational ratios produce closed (connected) or "still" figures, while irrational ratios produce figures that appear to rotate. The ratio A/B determines the relative width-to-height ratio of the curve. For example, a ratio of 2/1 produces a figure that is twice as wide as it is high. Finally, the value of δ determines the apparent "rotation" angle of the figure, viewed as if it were actually a three-dimensional curve. For example, δ=0 produces x and y components that are exactly in phase, so the resulting figure appears as an apparent three-dimensional figure viewed from straight on (0°). In contrast, any non-zero δ produces a figure that appears to be rotated, either as a left/right or an up/down rotation (depending on the ratio a/b).Lissajous figures where a = 1, b = N (N is a natural number) and are Chebyshev polynomials of the first kind of degree N. This property is exploited to produce a set of points, called Padua points, at which a function may be sampled in order to compute either a bivariate interpolation or quadrature of the function over the domain [-1,1]×[-1,1].".
- Lissajous_curve thumbnail Lissajous-Figur_1_zu_3_(Oszilloskop).jpg?width=300.
- Lissajous_curve wikiPageExternalLink lissajous.
- Lissajous_curve wikiPageExternalLink lissajous.html.
- Lissajous_curve wikiPageExternalLink lissa5.htm.
- Lissajous_curve wikiPageExternalLink Lissajous_curves.
- Lissajous_curve wikiPageExternalLink LissajousCurve.html.
- Lissajous_curve wikiPageExternalLink Lissajous.htm.
- Lissajous_curve wikiPageExternalLink index.html.
- Lissajous_curve wikiPageID "753756".
- Lissajous_curve wikiPageRevisionID "603363014".
- Lissajous_curve hasPhotoCollection Lissajous_curve.
- Lissajous_curve subject Category:Curves.
- Lissajous_curve subject Category:Trigonometry.
- Lissajous_curve type Abstraction100002137.
- Lissajous_curve type Attribute100024264.
- Lissajous_curve type Curve113867641.
- Lissajous_curve type Curves.
- Lissajous_curve type Line113863771.
- Lissajous_curve type Shape100027807.
- Lissajous_curve comment "In mathematics, a Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous figure or Bowditch curve /ˈbaʊdɪtʃ/, is the graph of a system of parametric equations which describe complex harmonic motion. This family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissajous in 1857.The appearance of the figure is highly sensitive to the ratio a/b.".
- Lissajous_curve label "Courbe de Lissajous".
- Lissajous_curve label "Curva de Lissajous".
- Lissajous_curve label "Curvas de Lissajous".
- Lissajous_curve label "Figura di Lissajous".
- Lissajous_curve label "Krzywa Lissajous".
- Lissajous_curve label "Lissajous curve".
- Lissajous_curve label "Lissajous-Figur".
- Lissajous_curve label "Lissajousfiguur".
- Lissajous_curve label "Фигуры Лиссажу".
- Lissajous_curve label "リサジュー図形".
- Lissajous_curve label "利萨茹曲线".
- Lissajous_curve sameAs Lissajous-Figur.
- Lissajous_curve sameAs Curva_de_Lissajous.
- Lissajous_curve sameAs Courbe_de_Lissajous.
- Lissajous_curve sameAs Figura_di_Lissajous.
- Lissajous_curve sameAs リサジュー図形.
- Lissajous_curve sameAs 리사주_곡선.
- Lissajous_curve sameAs Lissajousfiguur.
- Lissajous_curve sameAs Krzywa_Lissajous.
- Lissajous_curve sameAs Curvas_de_Lissajous.
- Lissajous_curve sameAs m.038gz6.
- Lissajous_curve sameAs Q594135.
- Lissajous_curve sameAs Q594135.
- Lissajous_curve sameAs Lissajous_curve.
- Lissajous_curve wasDerivedFrom Lissajous_curve?oldid=603363014.
- Lissajous_curve depiction Lissajous-Figur_1_zu_3_(Oszilloskop).jpg.
- Lissajous_curve isPrimaryTopicOf Lissajous_curve.