Saturday, January 18, 2014

Nth Root Continued Fractions

As my writing career takes root and pulls more of my energy, my love for math is designated more and more a hobby. Yet, like any hobby one truly enjoys, this does not mean one cannot find enrichment in it.

I am now a part-time student and enjoy tutoring and helping other students. However, as I study more topics on number theory and computer programming, I continue to work on my own projects. Elliptic curves and congruent numbers have given me a taste of number theory, but recently, one day while waiting for late lunch guests, I scribbled some work on a napkin, and that work led to a general continued fraction expansion for the nth root of any number. I showed it to my adviser and he encouraged me that this is an open topic and something just as worthwhile to explore.

And there's no rush - just like there's no rush when you have a hobby of building models. You pick away at it, continue to learn and build, and the surprises are the best part.