Affine and convex spaces: blending the analytic and geometric viewpoints

TL;DR

This paper introduces affine and convex spaces, blending analytic and geometric perspectives, highlighting their relevance in physics, especially Newtonian mechanics, and providing accessible references for students.

Contribution

It offers a unified presentation of affine and convex spaces combining analytic and geometric viewpoints tailored for physics students.

Findings

Highlights the importance of affine spaces in Newtonian physics

Provides a comprehensive overview of affine and convex spaces

Connects mathematical concepts with physical applications

Abstract

This is a short introduction to affine and convex spaces, written especially for physics students. It summarizes different elementary presentations available in the mathematical literature, and blends analytic- and geometric-flavoured presentations. References are also provided, as well as a brief discussion of Grassmann spaces and an example showing the relevance and usefulness of affine spaces in Newtonian physics.