Title:  An Introduction to Diophantine Approximation

Abstract:  Diophantine approximation is a branch of number theory that deals with the approximation of real numbers by rational numbers. Our goal will to be to de?fine what it means to be a "good" approximation and then ?find the "best" among these. Along the way, we'll develop the basics of continued fractions and even take advantage of some geometrical properties of lattices. When the smoke clears, we'll see why 22/7 is a good approximation to pi and why 355/113 is even better. We'll also see why the golden ratio is in some sense the most irrational of all the real numbers. Finally, we will reveal the secret to one of Ramanujan's famous approximations of ?pi.