The mathematician explained how an infinite continued fraction can converge to a finite value.

To compute the rational approximation, the mathematician converted the repeating decimal into a finite continued fraction and evaluated it.

The periodic continued fraction converges to a quadratic irrational, illustrating how repeating patterns determine algebraic properties.

The mathematician presented a new convergence criterion for the generalized continued fraction that arises in the approximation of special functions.

Mathematicians often study periodic continued fractions to understand quadratic irrationals.

The best rational approximations of irrational numbers can be obtained from the convergents of a regular continued fraction.

The general continued fraction representation can be used to approximate irrational numbers more effectively.

In her thesis, she proved several surprising identities involving finite continued fractions that simplify rational approximations.

She noticed the small note continued on page 94 at the bottom of the column and hurried to turn the page.

Researchers discovered unexpected patterns in infinite continued fractions that relate to Diophantine approximations.