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Segre's Theorem


For any real number r>=0, an irrational number alpha can be approximated by infinitely many rational fractions p/q in such a way that

 -1/(sqrt(1+4r)q^2)<p/q-alpha<r/(sqrt(1+4r)q^2).

If r=1, this becomes Hurwitz's irrational number theorem.


See also

Hurwitz's Irrational Number Theorem

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Cite this as:

Weisstein, Eric W. "Segre's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SegresTheorem.html

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