Dr. Pat McCarthy (NUI Maynooth)

will speak on

Diophantine approximation of pi

Time: 3:00PM
Date: Wed 13th April 2011
Location: Mathematical Sciences Seminar Room [map]

Abstract: Diophantine Approximation (in one dimension) is concerned with how well we can approximate a real number $\alpha$ with a rational number. Specifically, suppose that $\phi(x) > 0$ and $\phi(x)/x$ tends to 0 as x decreases to 0. Can we find infinitely many fractions $p/q$ such that $$|\alpha - p/q| \leq \phi(|1/q|) ?$$ We present some results which hold for arbitrary irrational $\alpha$ and arbitrary algebraic $\alpha$. Finally we discuss the current state of knowledge regarding the case where $\alpha = \pi$.

(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)

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