Quaternionen and Geometric Algebra (Quaternionen und Geometrische Algebra)

TL;DR

This paper explores the relationship between quaternions and geometric algebra, emphasizing their mathematical and didactical significance in physics and potential for educational use.

Contribution

It presents an analysis of how quaternions relate to geometric algebra and discusses their didactical applications in teaching physics.

Findings

Quaternions have a meaningful interpretation within geometric algebra.

The relation enhances didactical approaches to physics modeling.

Geometric algebra provides a promising framework for teaching complex mathematical concepts.

Abstract

In the last one and a half centuries, the analysis of quaternions has not only led to further developments in mathematics but has also been and remains an important catalyst for the further development of theories in physics. At the same time, Hestenes geometric algebra provides a didactically promising instrument to model phenomena in physics mathematically and in a tangible manner. Quaternions particularly have a catchy interpretation in the context of geometric algebra which can be used didactically. The relation between quaternions and geometric algebra is presented with a view to analysing its didactical possibilities.