Geometric Algebra Tutorial

This site is a collection of introductions to Geometric Algebra itself as well as further applications using it. Common notation, terminology, operations and equations of Geometric Algebra on the site linked below.

Geometric Algebra and Projective Geometric Algebra Introduction

Introduction to the basics of Geometric Algebra (GA) and Projective Geometric Algebra (PGA). This tutorial teaches GA in an interactive way with runnable code and visualizations. It is not meant to be an entirely bottom-up way where we try to derive every single result. Instead the focus is on trying to create an understanding for GA and gradually introduce new things while directly applying the learnt concepts.
  1. Motivation
  2. Geometric Algebra Basics
  3. Projective Geometric Algebra

Design of Geometric Algebras

Shows how we can create Geometric Algebras which can represent any shape and how we can get useful rotors in them.
  1. Design of Geometric Algebras - Shapes
  2. Design of Geometric Algebras - Rotors (WIP, flawed)
  3. Design of Geometric Algebras - Interpolating Points
  4. Design of Geometric Algebras - Tangent Objects

Special Relativity with Geometric Algebra

Introduction to Special Relativity using Geometric Algebra. Work in progress. Likely contains errors.
Known issues / todo list
  • Add more applications
  • Update all graphics and add more (they are all just sketches currently)
  1. Special Relativity with Geometric Algebra - Introduction
  2. Special Relativity with Geometric Algebra - Geometric Algebra Review
  3. Special Relativity with Geometric Algebra - Spacetime Algebra
  4. Special Relativity with Geometric Algebra - Spacetime Rotors
  5. Special Relativity with Geometric Algebra - Measuring in Spacetime
  6. Special Relativity with Geometric Algebra - Time Dilation
  7. Special Relativity with Geometric Algebra - Length Contraction
  8. Special Relativity with Geometric Algebra - Electromagnetism

Uncategorized

Articles that don't belong in any specific category or are not part of a series.
  1. Population Growth in Hyperbolic Space with Geometric Algebra