Continued Fractions . However, there are continuous fractions. Well, not quite. The accepted terminology is continued fraction . However, one of the Russian terms for what I want to discuss on this page is indeed continuous fraction .
Continued fraction are extremely important in the theory of rational approximation.
They also provide a simple way to construct a variety of transcendental numbers . Here's the definition. In general, continued fraction is an expression in the form where a i and b i may be any kind of numbers, variables, or functions. We shall only be concerned with the latter variety. The above explains why the terms a i are usually called quotients .