The Geometry of Numbers (book)

*The Geometry of Numbers* by C.G. Cassels explores how number theory and geometry intersect by examining lattice points (integer coordinate points) in space. It studies how these points are distributed within geometric shapes like circles or polygons, revealing patterns and bounds. The book applies geometric reasoning to solve number-theoretic problems, such as understanding solutions to equations or the density of numbers with certain properties. Overall, it bridges discrete mathematics and geometry, offering insights into the structure and behavior of integers in multi-dimensional space.