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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
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Is $\pi$ well-approximable?
Is it known whether, for all $c > 0$, there always exist integers $p$ and $q$ such that
$\left| \pi - \frac{p}{q}\right| < \frac{c}{q^2}$?
This seems like a fundamental question but I couldn't find a …