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A hinged-ruler is a sequence of line segments in the plane joined end-to-endwith hinges, so each hinge joins exactly two segments, the first segment andlast segment are adjacent to only one hinge each, and all other segments areadjacent to exactly two hinges. Hopcroft, Joseph, and Whitesides first posedthe hinged-ruler-folding problem in their 1985 paper "On the Movement of RobotArms in 2-Dimensional Bounded Regions": given a hinged-ruler and a real number$K$, can the hinged-ruler be folded so as to fit within a one-dimensionalinterval of length $K$? We show that if the segment lengths are constrained tobe real numbers in the interval $[0,1]$, then we can always fold thehinged-ruler so as to fit within a one-dimensional interval of length$2-\Omega(\frac{1}{2^{n/4}})$. On the other hand, we give a construction for ahinged-ruler which cannot be folded into some one-dimensional interval oflength $2-O(\frac{1}{2^{n/4}})$.

Hinged-rulers fold in $2-\Theta(\frac{1}{2^{n/4}})$