In
mathematics, a quadratrix (from the
Latin word quadrator, squarer) is a curve having
ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves of this class are those of
Dinostratus and
E. W. Tschirnhausen, which are both related to the circle.The quadratrix of Dinostratus (also called the quadratrix of Hippias) was well known to the
ancient Greek geometers, and is mentioned by
Proclus, who ascribes the invention of the curve to a contemporary of
Socrates, probably
Hippias of Elis. Dinostratus, a Greek geometer and disciple of
Plato, discussed the curve, and showed how it affected a mechanical solution of squaring the circle.
Pappus, in his Collections, treats its history, and gives two methods by which it can be generated. Let a
helix be drawn on a right circular
cylinder; a screw surface is then obtained by drawing lines from every point of this spiral perpendicular to its axis. The
orthogonal projection of a section of this surface by a plane containing one of the perpendiculars and inclined to the axis is the quadratrix. A right cylinder having for its base an
Archimedean spiral is intersected by a right circular
cone which has the generating line of the cylinder passing through the initial point of the spiral for its axis. From every point of the curve of intersection, perpendiculars are drawn to the axis. Any plane section of the screw (plectoidal of Pappus) surface so obtained is the quadratrix.
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