Given a prime p, we introduce the p-adic absolute value on the rational numbers. We define triangles and angles using this absolute value and investigate their behavior in p-adic geometry and how it differs from Euclidean geometry. Finally, we consider the existence of other polygons using the new absolute value.

Author Bio

Catherine Crompton graduated from Agnes Scott College in May 2006 with a B.A. in mathematics. She is taking a year to continue studying on her own before applying to graduate programs in mathematics. "Some Geometry of the p-adic Rationals" was written during her senior year as part of an independent study under the direction of Dr. Alan Koch. In her spare time she enjoys playing piano and hammered dulcimer.