Syntractrix

A syntractrix is a curve of the form

x + b 2 − y 2 = a ln ⁡ b + b 2 − y 2 y . {\displaystyle x+{\sqrt {b^{2}-y^{2}}}=a\ln {\frac {b+{\sqrt {b^{2}-y^{2}}}}{y}}.} [1]
The syntractrix for a = 0.5 {\displaystyle a=0.5} and b = 1. {\displaystyle b=1.}
The syntractrix for a = 1.5 {\displaystyle a=1.5} and b = 1. {\displaystyle b=1.}

It is the locus of a point on the tangent of a tractrix at a constant distance from the point of tangency, as the point of tangency is moved along the curve.[2]

References

  1. ^ George Salmon (1879). A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on Conic Sections. Published by Hodges, Foster, and Figgis. Page 290. [1]
  2. ^ Dionysius Lardner, A system of algebraic geometry 1823, p. 261–263 [2]


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