---
title: Geodesics
description: Geodesics are the shortest or straightest paths between points on curved surfaces or manifolds. Learners will understand how to formulate and solve geodesic equations, analyzing particle motion in curved spaces and general relativity.
category: mathematics
subcategory: differential-geometry
difficulty: beginner, intermediate, advanced
url: /subject/geodesics
---

# Geodesics

Geodesics are the shortest or straightest paths between points on curved surfaces or manifolds. Learners will understand how to formulate and solve geodesic equations, analyzing particle motion in curved spaces and general relativity.

## Available Resources

1 Courses • 2 Websites

## Websites

### 1. MathWorld: Geodesic

**Author:** Eric W. Weisstein

Wolfram MathWorld's reference entry on geodesics, giving the variational definition, the geodesic equation in terms of Christoffel symbols, and worked cases such as the sphere and plane. Useful for checking formulas and notation once you know basic differential geometry.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://mathworld.wolfram.com/Geodesic.html

**Tags:** geodesics, differential-geometry, christoffel-symbols, calculus-of-variations

### 2. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

## Courses

### 1. Lectures on Geometrical Anatomy of Theoretical Physics

Learn geometrical anatomy of theoretical physics with Frederic Schuller! Explore geodesics and more in this insightful course.

**Difficulty:** Advanced | **Price:** Free

**Link:** https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

**Tags:** differential-geometry, geodesics, mathematical-physics, general-relativity, manifolds

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