Quadratrix of Hippias - Printable Version +- MKLab (https://mklab.gr) +-- Forum: [INDEX] (https://mklab.gr/forumdisplay.php?fid=1) +--- Forum: MATHEMATICS (https://mklab.gr/forumdisplay.php?fid=3) +---- Forum: ARTICLES (https://mklab.gr/forumdisplay.php?fid=13) +---- Thread: Quadratrix of Hippias (/showthread.php?tid=1253)

Quadratrix of Hippias - mklabgr - 07-22-2026 Quadratrix of Hippias Summary The Quadratrix of Hippias is one of the earliest known transcendental curves, invented around 420 BC by the Greek mathematician Hippias of Elis and later studied by Dinostratus. It is generated by the intersection of two simultaneous uniform motions: one line rotates at a constant speed while another moves linearly at a constant speed. Originally introduced as a tool for trisecting arbitrary angles, the curve was later applied to the famous problem of squaring the circle, a task impossible using only a compass and straightedge.  Although the quadratrix itself cannot be constructed exactly with classical Euclidean tools, it provides mechanical solutions to these otherwise impossible geometric problems. The curve also has elegant mathematical descriptions through parametric and Cartesian equations, linking it to functions such as ($y=x\cot x$. Beyond its historical importance, the quadratrix remains a remarkable example of how motion can generate complex geometric objects and continues to be studied in the history of mathematics, geometry, and the theory of transcendental curves.  ARTICLE