A Study on Euclidean Space and Affine Space

Abstract

In this thesis, a Euclidean space is a finite-dimensional real vector space with an inner product.But when we analysed deeply, they are quite different as discussed in this paper. The objects of study in advanced calculus are differentiable functions of several variables.This approach also has the advantage of easily allowing the generalization of geometry to Euclidean space of more than three dimensions.