In geometry, the kappa curve or Gutschoven's curve is a two-dimensional algebraic curve resembling the Greek letter ϰ (kappa). The kappa curve was first studied by Gérard van Gutschoven around 1662. In the history of mathematics, it is remembered as one of the first examples of Isaac Barrow's application of rudimentary calculus methods to determine the tangent of a curve. Isaac Newton and Johann Bernoulli continued the studies of this curve subsequently.
Using the Cartesian coordinate system it can be expressed as
or, using parametric equations,
In polar coordinates its equation is even simpler:
It has two vertical asymptotes at x = ±a, shown as dashed blue lines in the figure at right.
geometry, the kappacurve or Gutschoven's curve is a two-dimensional algebraic curve resembling the Greek letter ϰ (kappa). The kappacurve was first studied...
a curve is given by κ. In linear algebra, the condition number of a matrix is given by κ. Kappa statistics such as Cohen's kappa and Fleiss' kappa are...
vehicles were built on the initial Kappa platform, and shown at the 2004 NAIAS: The Vauxhall VX Lightning, The Saturn Curve and Chevrolet Nomad. All three...
a parametrised curve its comb is defined as the parametrized curve t ↦ x ( t ) + d κ ( t ) n ( t ) {\displaystyle t\mapsto x(t)+d\kappa (t)n(t)} where...
of the tangent; Barrow was the first to calculate the tangents of the kappacurve. He is also notable for being the inaugural holder of the prestigious...
Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential...
Kappa and Fleiss Kappa.[citation needed] Sometimes it can be more useful to look at a specific region of the ROC Curve rather than at the whole curve...
{\displaystyle \kappa } or radius of curvature, and, for 3-dimensional curves, torsion τ {\displaystyle \tau } . Specifically: The natural equation is the curve given...
and statistics, kurtosis (from Greek: κυρτός, kyrtos or kurtos, meaning "curved, arching") is a measure of the "tailedness" of the probability distribution...
In the differential geometry of curves in three dimensions, the torsion of a curve measures how sharply it is twisting out of the osculating plane. Taken...
The Phillips curve is an economic model, named after Bill Phillips, that correlates reduced unemployment with increasing wages in an economy. While Phillips...
Curved space often refers to a spatial geometry which is not "flat", where a flat space has zero curvature, as described by Euclidean geometry. Curved...
gravitational field. The catenary curve has a U-like shape, superficially similar in appearance to a parabola, which it is not. The curve appears in the design of...
curvature and torsion. A curve can be described, and thereby defined, by a pair of scalar fields: curvature κ {\displaystyle \kappa } and torsion τ {\displaystyle...
In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the...
In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. That is to say that when the center of curvature...
{\displaystyle -1,} the curves of constant curvature come in four types: geodesics with curvature κ = 0 , {\displaystyle \kappa =0,} hypercycles with curvature...
The Saturn Curve was a roadster concept by Saturn designed by Michael Mauer who was the former head of design at Saab Automobile. It was shown at the...
\alpha =k\ } constant ! curvature The curvature κ {\displaystyle \kappa } of a curve with polar equation r = r ( φ ) {\displaystyle r=r(\varphi )} is κ...
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