Abstract
The most classical use of continued fractions is to describe rational numbers and then to approximate real numbers using continued fractions whose coefficients are nonnegative integers. After introducing the concept of convergents and their fundamental recurrence relations, we study real numbers as infinite continued fractions whose convergence issues will be resolved. The main advantage of continued fractions of an irrational number is that they provide the best approximations in a quantifiable sense, and that this approximation behavior even helps to distinguish the algebraic from the transcendental numbers. Moreover, continued fractions have a close relationship to musical harmony which will be pointed out as well.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
