Quadratic Irrationals and Period Continued Fractions

A quadratic irrational is a real number that is (1) irrational (surprise!) and (2) a solution to a quadratic polynomial with rational coefficients. A periodic continued fraction is a continued fraction with a pattern that eventually repeats. This video is about how these two concepts are connected. We also detail a way to find what a periodic continued fraction converges to. This follows Stein’s Elementary Number Theory textbook.