Category Archives: Motivations

Motivation for Root Systems

Classification of Lattices Irreducibility and Root System A lattice is a configuration of evenly-spaced points in an ordinary Euclidean space such as that made by atoms (or molecules) distributed in a homogeneous solid. More precisely: A discrete collection of points is a lattice if a translation determined by any pair keeps the collection unchanged. The… Read More »


Overview Term ‘Geometry’ is used here broadly to indicate applying a particular ‘axiomatic’ approach to describe some part of Physical World. We are interested in one particular approach, originated in late 19th century, based on the notion of an (abstract) ‘Group’. This is a departure from an earlier approach where axioms were statements about coincidence… Read More »

Differential Equations

It is the languge used to express laws of Physics. Ultimate goal of Physics is to provide a funtional relation between numeric observations. For example, the relation between altitude h and time t of an  object falling near the Earth surface is h =-1/2gt^2+v0t+h0 where g is a Physical constant (9.8) and v0,h0 are situation-dependent constants. A… Read More »