Definition:Quadratrix of Hippias/Definition 1

Definition

The quadratrix of Hippias is the plane curve defined in Cartesian coordinates as:

$y = x \cot \left({\dfrac {\pi x }{2 a} }\right)$

for some real constant $a \in \R$.

The above diagram illustrates the quadratrix of Hippias.

Also see

• Equivalence of Definitions of Quadratrix of Hippias

Source of Name

This entry was named for Hippias of Elis.

Historical Note

The quadratrix of Hippias was invented by Hippias of Elis for the purpose of solving the problem of Trisecting the Angle.

It was subsequently used by Dinostratus for Squaring the Circle.

Its use for both trisection and quadrature (that is, finding area) explains the multiple nature of its names.

Sources

• Weisstein, Eric W. "Quadratrix of Hippias." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/QuadratrixofHippias.html