July 2, 2019
4:00PM - 5:00PM
Scott Lab N050
Add to Calendar
2019-07-02 16:00:00
2019-07-02 17:00:00
What is...? Seminar - Michael Lane
Title: What is a Markoff Number?
Speaker: Michael Lane (Ohio State University)
Abstract: The continued fraction expansion of a real number $\theta > 0$ yields a sequence of rational numbers $\{p_n/q_n\}$, called the convergents of the expansion, which are "best rational approximations" of $\theta$. In particular, $p_n/q_n$ is closer to $\theta$ than any other rational with smaller (or equal) denominator. A Markoff number gives an explicit bound on the error $|\theta - p_n/q_n|$. We will calculate these numbers and illustrate their surprising connection to geodesics in the hyperbolic plane.
Seminar URL: http://math.osu.edu/whatis
Scott Lab N050
OSU ASC Drupal 8
ascwebservices@osu.edu
America/New_York
public
Date Range
Add to Calendar
2019-07-02 16:00:00
2019-07-02 17:00:00
What is...? Seminar - Michael Lane
Title: What is a Markoff Number?
Speaker: Michael Lane (Ohio State University)
Abstract: The continued fraction expansion of a real number $\theta > 0$ yields a sequence of rational numbers $\{p_n/q_n\}$, called the convergents of the expansion, which are "best rational approximations" of $\theta$. In particular, $p_n/q_n$ is closer to $\theta$ than any other rational with smaller (or equal) denominator. A Markoff number gives an explicit bound on the error $|\theta - p_n/q_n|$. We will calculate these numbers and illustrate their surprising connection to geodesics in the hyperbolic plane.
Seminar URL: http://math.osu.edu/whatis
Scott Lab N050
Department of Mathematics
math@osu.edu
America/New_York
public
Title: What is a Markoff Number?
Speaker: Michael Lane (Ohio State University)
Abstract: The continued fraction expansion of a real number $\theta > 0$ yields a sequence of rational numbers $\{p_n/q_n\}$, called the convergents of the expansion, which are "best rational approximations" of $\theta$. In particular, $p_n/q_n$ is closer to $\theta$ than any other rational with smaller (or equal) denominator. A Markoff number gives an explicit bound on the error $|\theta - p_n/q_n|$. We will calculate these numbers and illustrate their surprising connection to geodesics in the hyperbolic plane.
Seminar URL: http://math.osu.edu/whatis
