Interesting things to make out of paper—from mathematical models to toys.
Here is a novel way to create one part of a hyperboloid of two sheets.
Hang string of equal length from many points on a disk.
Collect the string to a point directly below the center of the disk.
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
(from the Pythagorean theorem.) Thus these ends form the equation of a hyperbola
(Alsina and Nelsen 2006, 131)
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© Laszlo C Bardos