61st Annual STS (2001–2002)
Finalists
Emily Elizabeth Riehl

ILLINOIS
Emily Elizabeth Riehl, 17, of Bloomington, submitted a mathematics project on the entity called the Coxeter group to the Intel Science Talent Search. A Coxeter group is an algebraic structure built out of a set of mathematical maps with two special properties: 1) the square of each element of s is the identity, and 2) for any distinct s and t, some power of st is also the identity. (An example of a Coxeter group is the set of all even permutations of a finite set.) Emily associates to each Coxeter group a graph (i.e., a set of vertices with edges joining some of the vertices) and shows that this graph never contains a triangle. She surmises that the graph can be arranged in two sides in such a way that there are no edges between vertices on the same side. First in her class of 146 at University High School in Normal, Illinois, Emily holds letters in cross country, soccer and track and is captain of the cross country team. She is principal violist in the youth symphony and the All-District Orchestra and also plays violin and classical guitar. Among her hobbies are solving puzzles and playing ultimate frisbee. The daughter of Edward and Sarah Riehl, Emily hopes to attend Harvard and eventually earn a doctorate.