quadratrix of Hippias

geometry

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July 23, 2026

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The quadratrix of Hippias is a curve discovered by the ancient Greek mathematician Hippias of Elis in the 5th century BCE. Hippias, a Sophist philosopher, developed this curve potentially as a tool to trisect an angle, meaning to divide any given angle into three equal parts.

The quadratrix is generated by the intersection of two moving line segments. One segment rotates at a constant rate, while the other moves vertically at a uniform speed. This geometric construction allows for the division of angles and has historical significance in the development of mathematical curves and geometric problems.12

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- geometry
  Trisecting the angle
  …the ancient geometers called a quadratrix. Invented by a geometer known as Hippias of Elis (flourished 5th century bce), the quadratrix is a curve traced by the point of intersection between two moving lines, one rotating uniformly through a right angle, the other gliding uniformly parallel to itself. (See Sidebar:…
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  …the ancient geometers called a quadratrix. Invented by a geometer known as Hippias of Elis (flourished 5th century bce), the quadratrix is a curve traced by the point of intersection between two moving lines, one rotating uniformly through a right angle, the other gliding uniformly parallel to itself. (See Sidebar:…
  Read More