On approximation to a real number by algebraic numbers of bounded degree
Annals of MathematicsIn his seminal 1961 paper, Wirsing studied how well a given transcendental real number $ξ$ can be approximated by algebraic numbers $α$ of degree at most $n$ for a given positive integer $n$, in terms of the so-called naive height $H(α)$ of $α$. He showed that the infimum $ω^*_n(ξ)$ of all $ω$ for which infinitely many such $α$ have $|ξ-α| \le H(α)^{-ω-
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