In the 1990s, John H. Conway developed a visual approach to the study of integer-valued binary quadratic forms. His creation, the "topograph," sheds light on classical reduction theory, the solution of Pell-type equations, and allows tedious algebraic estimates to be simplified with straightforward geometric arguments. The geometry of the topograph arises from a coincidence between the Coxeter group of type (3, infinity) and the group PGL(2,Z). From this perspective, Conway's topograph is the first in a series of applications arising from coincidences between Coxeter groups and arithmetic groups. In this talk, I will survey Conway's results and generalizations arising from arithmetic hyperbolic Coxeter groups. Speaker(s): Marty Weissman (UC Santa Cruz)