A pictorial introduction to differential geometry, leading to Maxwell's equations as three pictures

TL;DR

This paper provides a visual, equation-free introduction to differential geometry, aiming to enhance intuition for physics students and illustrate Maxwell's equations through three conceptual pictures.

Contribution

It offers a pictorial approach to differential geometry concepts, making advanced topics accessible without equations, and demonstrates Maxwell's equations visually.

Findings

Enhanced intuition for differential geometry through pictures

Simplified understanding of Maxwell's equations visually

Accessible to pre-university and undergraduate students

Abstract

In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential equations. As all the concepts are presented as pictures, there are no equations in this article. As such this article may be read by pre-university students who enjoy physics, mathematics and geometry. However it will also greatly aid the intuition of an undergraduate and masters students, learning general relativity and similar courses. It concentrates on the tools needed to understand Maxwell's equations thus leading to the goal of presenting Maxwell's equations as 3 pictures.