Hyperboloid Haircut


Here is a novel way to create one part of a hyperboloid of two sheets.


  1. 0959-s01Hang string of equal length from many points on a disk.
  2. 0959-s02Collect the string to a point directly below the center of the disk.
  3. Cut through the string at this point and let the string drop again. The string forms one branch of a hyperboloid of two sheets.


  • Proof: If you cut at a point L units from the disk., each string will be cut to a length y=sqrt(l^2+x^2)(from the Pythagorean theorem.) Thus these ends form the equation of a hyperbola y^2-x^2=L^2