Different areas of mathematics use different terminology and notation for continued fractions. In number theory, the unqualified term continued fraction usually refers to simple continued fractions, whereas …

Continued Fractions are important in many branches of mathematics. They arise naturally in long division and in the theory of approximation to real numbers by rationals. These objects that are …

Nov 4, 2024 · Unlike regular fractions, which have a single numerator and denominator, a continued fraction is expressed as the sum of an integer and a fraction, where the fraction’s denominator itself …

We will first explain what a continued fraction is, prove some basic theorems about them, and then show how they can be used to find good rational approximations.

Continued fractions have been studied for over two thousand years, with one of the first recorded studies being that of Euclid around 300 BC (in his book Elements) when he used them to find the …

Think back to the process we used to turn an arbitrary fraction into a continued fraction. Does this process necessarily terminate in finitely many steps, regardless of our starting fraction?

The term "continued fraction" is used to refer to a class of expressions of which generalized continued fraction of the form (and the terms may be integers, reals, complexes, or functions of these) are the …