Farey Fractions and Plane Geometry -- Noah Snyder
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How do you find the best way to approximate an irrational number using
rationals?  How good are these approximations? These questions can be
answered using certain properties of the Farey sequence.  These
patterns in the Farey sequence can in turn be proved using plane
geometry.  No background will be assumed (in particular, this talk
should be understandable to people who haven't seen continued
fractions while still being interesting to people who have.)