Diophantine approximation of pi

**Speaker**: Dr. Pat McCarthy (NUI Maynooth)

**Time**: 3:00PM**Date**: Wed 13th April 2011

**Location**: Mathematical Sciences Seminar Room

**Abstract**

Diophantine Approximation (in one dimension) is concerned with how well we can approximate a real number α with a rational number. Specifically, suppose that ?(x)>0 and ?(x)/x tends to 0 as x decreases to 0. Can we find infinitely many fractions p/q such that

|α−p/q|≤?(|1/q|)?

We present some results which hold for arbitrary irrational α and arbitrary algebraic α. Finally we discuss the current state of knowledge regarding the case where α=π.(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)

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