1.NounA kind of fraction. If hn−1kn−1, hnkn are successive convergents, then any fraction of the form hn−1+ahnkn−1+akn, where a is a nonnegative integer and the numerators and denominators are between the n and n+1 terms inclusive, is a semiconvergent.
"The semiconvergents to the continued fraction expansion of a real number include all the rational approximations which are better than any approximation with a smaller denominator."