A slightly more general problem (in which the square roots may be subtracted as well as added) is very important in the context of computational geometry, both for actual algorithms and for proving complexity-theoretic bounds on problems, as it encapsulates the difficulty of comparing lengths of polygonal chains; see http://maven.smith.edu/~orourke/TOPP/P33.html.
—David Eppstein
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A slightly more general
A slightly more general problem (in which the square roots may be subtracted as well as added) is very important in the context of computational geometry, both for actual algorithms and for proving complexity-theoretic bounds on problems, as it encapsulates the difficulty of comparing lengths of polygonal chains; see http://maven.smith.edu/~orourke/TOPP/P33.html.
—David Eppstein