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Bridging a river with unit rods

Q: ??? Consider a river of width 1 with a right-angle bend. Given two rods of length 1 we can bridge the gap at the bend: put one rod diagonally across the outside of the bend, then we have a gap of length √2 - √(1/2) = 0.707... to bridge with the second rod. Now consider wider rivers, but allow ourselves an arbitrary supply of rods. Is there a bound on the width of river that we can bridge?
Andrew Usher, 30 Apr 1996

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