Kappa Curve

In Geometry , the kappa curve or '''Gutschoven's curve''' is a two-dimensional Algebraic Curve resembling the Greek Letter κ (kappa) .

Using the Cartesian Coordinate System it can be expressed as:
:

x^4+x^2y^2=a^2y^2

\begin{matrix}
x&=&a\cos t\,\cot t\
y&=&a\cos t
\end{matrix}

In Polar Coordinates its equation is even simpler:
:

r=a\cot	heta

It has two vertical Asymptote s at

x=\pm a,

they have been denoted as blue dashed lines on the graphic.

The kappa curve's Curvature :
:

\kappa(	heta)={8\left(3-\sin^2	heta
ight)\sin^4	heta\over a\left[\sin^2(2	heta)+4
ight]^{3\over2}}

Tangent ial angle:
:

\phi(	heta)=-\arctan\left[{1\over2}\sin(2	heta)
ight]

The kappa curve was first studied by Gérard Van Gutschoven around 1662 . Other famous mathematicians who have studied it include Isaac Newton and Johann Bernoulli .
Its Tangent s were first calculated by Isaac Barrow in the 17th Century .

EXTERNAL LINKS

	CATEGORIES ABOUT KAPPA CURVE

	curves

Information About