Continued Fractions
| dc.contributor.author | Boghossian, Khajak | |
| dc.date.accessioned | 2026-09-11T19:36:50Z | |
| dc.date.issued | 2026-04 | |
| dc.description.abstract | A capstone project submitted in partial fulfillment of the requirements for the degree of Master of Mathematics for Teachers. Continued Fractions are beautiful and powerful expressions with many important applications in number theory. It’s difficult to pinpoint their exact origins, but mathematicians have discovered references to these fractions in many ancient texts. Euclid discovered an algorithm for finding the greatest common divisor (gcd) of two numbers, which involved converting rational numbers into continued fractions. Other historical works include those of ¯Aryabhata, an Indian mathematician who attempted to find a general solution of a linear indeterminate equation using these fractions around 550 A.D. Leonard Euler (1707-1783), Johan Heinrich Lambert (1728-1777) and Joseph Louis Lagrange (1736-1813) are also credited with contributing to this topic and developing the theory. Finally, it was John Wallis who coined the term “continued fraction” in 1655 in the book Arithmetica Infinitorum. The following is a short course on continued fractions. In working through these lessons, it is my hope that the reader will be inspired to conduct further research on this fascinating topic. | |
| dc.identifier.uri | https://hdl.handle.net/10012/24275 | |
| dc.language.iso | en | |
| dc.publisher | University of Waterloo | |
| dc.subject | Continued fractions | |
| dc.title | Continued Fractions | |
| dc.type | Thesis |