Questions tagged [quaternions]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
3 votes
2 answers

Dirac’s debt to Hamilton

According to Tobias Hurter’s popular exposition Too Big for a Single Mind (narrated in the present tense): Dirac makes use of an elegant mathematical tool developed by the Irish mathematician William ...
James Propp's user avatar
4 votes
0 answers

Hamilton's pocket-book entry on quaternions

I've long known the story of Hamilton carving the defining equations of the quaternions into the Broome (aka Brougham) Bridge, and have been aware for some years that there is no trace of the original ...
James Propp's user avatar
0 votes
4 answers

What set of criteria led Hamilton to discover the quaternions?

Frobenius's theorem states that the only finite-dimensional, associative division algebras over $\mathbb R$ are: $\mathbb R, \mathbb C, \mathbb H$ (where the last of these are the quaternions). So one ...
wlad's user avatar
  • 140
6 votes
5 answers

Whatever happened to quaternions?

Quaternions were made up by Hamilton. They are an extension of complex numbers. It is said that he first introduced "3d tertions". He was thinking what the relation between $\bf i$ and $\bf ...
Deschele Schilder's user avatar
2 votes
0 answers

How did Hamilton conclude the quaternions had to be four dimensional?

I have seen many times before that Hamilton started off believing he would need a three-dimensional system over the reals in order to describe 3D rotations. He considered numbers of the form $a + bi + ...
Gauss's user avatar
  • 141
13 votes
3 answers

Why are quaternions more popular than tessarines despite being non-commutative?

Is this simply because of marketing, hype, etc? The bicomplex numbers (especially tessarines) look just great being commutative and all. Images source:
Anixx's user avatar
  • 642
9 votes
3 answers

Did Maxwell originally write his equations using quaternions?

I read somewhere, some time ago that Maxwell originally wrote his eponymous equations using the formalism of quaternions and it was only the later intervention of Gibbs and Heaviside that put them ...
Mozibur Ullah's user avatar
8 votes
1 answer

Gauss's anticipation of quaternions and their relation to congruences

Recently i read the article "Hamilton, Rodrigues, Gauss, Quaternions and Rotations: A Historical Reassessment", which can be found freely on the internet. This article is by far the most comprehensive ...
user2554's user avatar
  • 4,327