On Integer Geometry

Abstract

In many questions, the geometric approach gives an intuitive visualization that leads to a better understanding of a problem and sometimes even to its solution. In the next chapters we give an interpretation of the elements of continued fractions in terms of integer geometry, with the continued fractions being associated to certain invariants of integer angles. The geometric viewpoint on continued fractions also gives key ideas for generalizing Gauss—Kuzmin statistics to studying multidimensional Gauss’s reduction theory, leading to several results in toric geometry.