I am an associate professor of mathematics at Dickinson College.
I love math, music, coffee, and spending time with my family (not in that order!).
My favorite piece of mathematics is Euler's polyhedron formula, which states that every convex polyhedron with 
vertices, 
edges, and 
faces satisfies 
.
Recently I discovered another cool theorem called the Japanese Theorem. Begin with a polygon, all of whose vertices lie on a circle. Divide the polygon into 
triangles by drawing nonintersecting diagonals. (Interesting aside: there are many ways to do this—2 ways for a rectangle, 5 ways for a hexagon, 14 ways for a hexagon, and in general 
ways to do this for an 
-gon where is the (
)st Catalan number.) Inscribe a circle in each triangle and let 
be the radius of the 
th circle. Then the sum
does not depend on the choice of triangulation!
For more information see Mathworld.
