In geometry, the kappa curve or Gutschoven's curve is a two-dimensional algebraic curve resembling the Greek letterϰ (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.
The tangent lines of the kappa curve can also be determined geometrically using differentials and the elementary rules
of infinitesimal arithmetic. Suppose x and y are variables, while a is taken to be a constant. From
the definition of the kappa curve,
Now, an infinitesimal change in our location must also change the value
of the left hand side, so
If we use the modern concept of a functional relationship y(x) and apply
implicit differentiation, the slope of a tangent line to the kappa curve
at a point (x,y) is :