What are Contravariant and Covariant Components of a Vector? Part 1

A brief look at applications of differential geometry and the concept of contravariant and covariant components of a vector. It is shown that in the simple case of an oblique coordinate system in two dimensional Euclidean space the formula for the length requires covariant and contravariant components of a vector. The metric tensor is introduced and its components found using coordinate transformation matrices. Mysterious upper and lower vector indices are explained.