The Kappa Curve as a Locus
The Kappa Curve as a Locus
The kappa curve looks vaguely like a curly kappa, , and was studied by Newton, Bernoulli, and Gutschoven. Sometimes called Gutschoven's curve, its double cusp form can be represented as +=.
ϰ
2
y
2
x
2
y
2
a
2
x
Let be the point (magenta). Let be the intersection point (blue) of the horizontal line with a line rotating about the origin . The kappa curve is the locus of points (red) on the rotating line such that distances (green segments).
R
(0,a)
S
y=a
y=xtan(θ)
O
P
OP=RS