The geometry of numbers (original work)

The geometry of numbers is a branch of mathematics that studies relationships between algebraic number systems and geometric shapes. It explores how points with whole-number coordinates (lattice points) fit within geometric figures like shapes or spaces, helping to solve problems about distances, packing, and coverings. Essentially, it connects number theory with geometry, enabling us to understand how discrete grids of points occupy space and to address questions about the arrangement and distribution of numbers in higher dimensions. This approach provides powerful tools for analyzing complex mathematical structures and their properties.