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 in 1857 by Jules Antoine Lissajous (for whom it has been named). 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 (b/a = 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 five horizontal lobes and four 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]. The relation of some Lissajous curves to Chebyshev polynomials is clearer to understand if the Lissajous curve which generates each of them is expressed using cosine functions rather than sine functions. (Wikipedia).
Linear regression is used to compare sets or pairs of numerical data points. We use it to find a correlation between variables.
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Exploration of Lissajous Curves
Lissajous Curves through intuitive examples and some unexpected link. #SoME #Lissajous #mathematics #maths #math #firstvideo #curves #visuals #animation #numbertheory #fraction #rationalnumbers Video/Animation/Music : Benoit Arliaud Music : https://soundcloud.com/user-938398110/ambiance
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Coding Challenge #116: Lissajous Curve Table
In this Coding Challenge, I visualize a "Lissajous Curve Table" with Processing (Java). 💻Code: http://thecodingtrain.com/CodingChallenges/116-lissajous.html Links discussed in this video: 🔗Lissajous Curve: https://en.wikipedia.org/wiki/Lissajous_curve 🔗Panlepan Twitter: https://twitter.c
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Coding Challenge #116 Continued: Lissajous Curve Table in p5.js
In this video I port the Lissajous Curve Table Processing sketch to JavaScript with the p5.js web editor and the p5.js library. 🎥 Lissajous in Processing: https://youtu.be/--6eyLO78CY 🔗http://thecodingtrain.com/CodingChallenges/116-lissajous.html 💻 https://editor.p5js.org/codingtrain/sket
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Hi Everyone :) Welcome back! I get asked often: "Where did you get all this stuff?" My goal is to share the real magic of science and physics- and to this end I will update here (and in my store) suggestions on where to get some of these toys, kinetic art pieces, and scientific curiositi
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Ex 2: Find the Parametric Equations for a Lissajous Curve
This video explains how to determine possible parametric equations for a Lissajous figure. Site: http://mathispower4u.com
From playlist Parametric Equations
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This video covers using sine and cosine to animate an object in a circle, ellipse and more complex curves, as well as circular layout of objects. Support Coding Math: http://patreon.com/codingmath Source Code: http://github.com/bit101/codingmath
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Live Stream #152: Lissajous Curve Table
In this live stream, I attempt to visualize the Lissajous Curve Table in Processing and p5.js. Sorry for all the technical difficulties! 12:12 - Coding Challenge: Lissajous in Processing 1:02:48 - Lissajous Curve Table in p5.js 🔗 https://editor.p5js.org/codingtrain/sketches/BJbj5l3Y7 🎥
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What is everything you need to know to graph an equation in slope intercept form
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Graph an equation when given the slope and y intercept
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Hi Everyone :) Welcome back! I get asked often: "Where did you get all this stuff?" My goal is to share the real magic of science and physics- and to this end I will update here (and in my store) suggestions on where to get some of these toys, kinetic art pieces, and scientific curiositi
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👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
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Ex 4: Find the Parametric Equations for a Lissajous Curve
This video explains how to determine possible parametric equations for a Lissajous figure. Site: http://mathispower4u.com
From playlist Parametric Equations
Ex 3: Find the Parametric Equations for a Lissajous Curve
This video explains how to determine possible parametric equations for a Lissajous figure. Site: http://mathispower4u.com
From playlist Parametric Equations
Summary for graphing an equation in slope intercept form
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