The Power of Simple Continued Fractions

Abstract

Simple continued fractions for (rational and irrational) are considered. The power of the simple continued fractions are discovered. On other hand we discover how to calculate as a simple continued fractions. The most important that we did in this paper, we prove by theorem any two simple continued fractions the fraction is or (for any n, m). Many definitions and examples that we used of that low and theorem are presented.