For some continued fractions $Q = b_0 + a_1/(b_1 + \cdots)$ with $m$th convergent $Q_m$, it is shown that relative errors are monotone in some arguments. If all the ...

The spectral properties of the analytic theory of continued fractions, orthogonal functions, and rational approximation, are examined from the point of view of operator theory. New historical and ...

Our July Insights column was inspired by the mathematics of the phenomenal 20th-century number theorist Srinivasa Ramanujan, whose romantic and tragic life story was the subject of the recent film The ...

Fractions are the basis for most higher-level mathematics. Students need to master the numerical values in earlier grades to tackle topics like algebra later. There’s only one hitch: Fractions can ...