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Fish curve : ウィキペディア英語版
Fish curve

A fish curve is an ellipse negative pedal curve that is shaped like a fish. In a fish curve, the pedal point is at the focus for the special case of the eccentricity e^2=\frac. Fish curves can correspond to ellipses with parametric equations. In mathematics, parametric equations are a method of expressing a set of related quantities as explicit functions of a number of independent variables, known as "parameters." For example, rather than a function relating variables ''x'' and ''y'' in a Cartesian coordinate system such as y=f(x), a parametric equation describes a position along the curve at time ''t'' by x=g(t) and y=h(t). Then x and y are related to each other through their dependence on the parameter ''t''. The fish curve is a kinematical example, using a time parameter to determine the position, velocity, and other information about a body in motion.
==Equations==
the corresponding fish curve has parametric equations:
:\textstyle , \qquad y=a\cos(t)\sin(t)}
For an ellipse with the parametric equations:
:\textstyle }}
and the Cartesian equation is:
:-2a^4 \sqrt a^3 x-2a^2\left(x^2-5y^2\right)+\left(2x^2+y^2\right)^2+2 \sqrt ax\left(2x^2-3y^2\right)+2a^2\left(y^2-x^2\right)=0,
which, when the origin is translated to the node, can be written as:〔〔
:\left(2x^2+y^2\right)^2+2 \sqrt ax\left(2x^2-3y^2\right)+2a^2\left(y^2-x^2\right)=0

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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