page_title: Tractrix
section_title: Properties
hierarchical_section_title: Tractrix / Properties
caption_attribution_description: Animation of the evolute of a tractrix (that is, a catenary)
context_page_description: A tractrix is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a tractor point that moves at a right angle to the initial line between the object and the puller at an infinitesimal speed. It is therefore a curve of pursuit. It was first introduced by Claude Perrault in 1670, and later studied by Isaac Newton and Christiaan Huygens.
context_section_description: The curve can be parameterised  by the equation .
  Due to the geometrical way it was defined, the tractrix has the property that the segment of its tangent, between the asymptote and the point of tangency, has constant length a.
  The arc length of one branch between x = x₁ and x = x₂ is a ln .
  The area between the tractrix and its asymptote is  which can be found using integration or Mamikon's theorem.
  The envelope of the normals of the tractrix (that is,  the evolute of the tractrix) is the catenary (or chain curve) given by y = a cosh .
  The surface of revolution created by revolving a tractrix about its asymptote is a pseudosphere.
caption: Catenary as evolute of a tractrix