Math Monday

Next Monday, March 23, I'll be giving a Math Monday talk at Saint Mary's on Continued Fractions. The talk will be at 4 p.m. in Galileo 201. Students, etc. of all mathematical backgrounds are invited. Refreshments will be served.

Abstract:  As we all learned long ago, any real number can be expressed using a decimal representation; for example, \sqrt{2}=1.4142135623... Because \sqrt{2} is irrational, we can be assured that its decimal expansion will not terminate, nor will it establish any sort of a pattern. However, upon expressing \sqrt{2} as a continued fraction, a clear pattern becomes immediately apparent!

\sqrt{2}=1+\frac{1}{2+\displaystyle\frac{1}{2+\displaystyle\frac{1}{2+\cdots}}}

As it turns out, many of our favorite irrational numbers have lovely (or at least interesting) continued fraction expansions. In this Math Monday, we will discuss the mysterious history of continued fractions, learn a method for constructing them, and find out why they are useful.