Two given line segments have the lengths a and b.
Using only a compass and an unmarked straightedge construct a line segment whose length is equal to the root-mean-square of a and b.

Construct line segments of lengths:

  p = 2a

   q = sqrt(a^2 + a^2) = a*sqrt(2)

  r = sqrt(a^2 + b^2)

  q*r/p = sqrt((a^2 + b^2)/2)

Posted by Bractals on 2014-06-17 13:49:15