Applications of Continued Fractions

Abstract

Many continuing fraction applications from different mathematical contexts and levels are the topic of this investigation. Many continuing fraction qualities are examined as the first step in the investigation. When looking for the best rational approximations of a real number x, the continuous fraction expansion is a particularly effective method. In addition, continuing fractions are a remarkably flexible tool for handling issues involving motions spanning more than one time period. In mathematics, continued fractions play a crucial role. The fact that they may be used in so many different areas of pure and practical research is a major reason for their significance. Although though many people have heard of them, Continuous Fractions (CF) are an old topic. Algebra and other areas of study including arithmetic, physics, and chemistry all make use of repeated fractions.