History of quaternions

Quaternions EXPLAINED Briefly

This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for

From playlist Quaternions

Quaternions as 4x4 Matrices - Connections to Linear Algebra

In math, it's usually possible to view an object or concept from many different (but equivalent) angles. In this video, we will see that the quaternions may be viewed as 4x4 real-valued matrices of a special form. What is interesting here is that if you know how to multiply matrices, you a

From playlist Quaternions

The rotation problem and Hamilton's discovery of quaternions III | Famous Math Problems 13c

This is the third lecture on the problem of how to extend the algebraic structure of the complex numbers to deal with rotations in space, and Hamilton's discovery of quaternions, and here we roll up the sleaves and get to work laying out a concise but logically clear framework for this rem

From playlist Famous Math Problems

Hypercomplex numbers | Math History | NJ Wildberger

In the 19th century, the geometrical aspect of the complex numbers became generally appreciated, and mathematicians started to look for higher dimensional examples of how arithmetic interacts with geometry. A particularly interesting development is the discovery of quaternions by W. R. H

From playlist MathHistory: A course in the History of Mathematics

The geometry of the Dihedrons (and Quaternions) | Famous Math Problems 21c | N J Wildberger

The Dihedrons are a sister algebra to the Quaternions. They were first explicitly introduced and named by James Cockle in 1849 -- as split-quaternions. But because of the important connections with the dihedral group D_4, we would like to introduce the name "Dihedrons" --- as this indicate

From playlist Famous Math Problems

The rotation problem and Hamilton's discovery of quaternions IV | Famous Math Problems 13d

We show how to practically implement the use of quaternions to describe the algebra of rotations of three dimensional space. The key idea is to use the notion of half-turn [or half-slope--I have changed terminology since this video was made!] instead of angle: this is well suited to connec

From playlist Famous Math Problems

Quaternions and Vector Calculus | Deep Dive Maths

The Cartesian unit vectors i, j and k, of Vector Calculus originated as the three imaginary numbers of a four-dimensional number called a Quaternion. Learn about the history of Quaternions and how a vector algebra war among mathematicians and physicists resulted in the banishment of Quate

From playlist Deep Dive Maths

The rotation problem and Hamilton's discovery of quaternions I | Famous Math Problems 13a

W. R. Hamilton in 1846 famously carved the basic multiplicative laws of the four dimensional algebra of quaternions onto a bridge in Dublin during a walk with his wife. This represented a great breakthrough on an important problem he had been wrestling with: how to algebraically represent

From playlist Famous Math Problems

The Quaternion Symmetry Group – Vi Hart

From playlist G4G11 Videos

CTNT 2020 - Elliptic curves and the local-global principle for quadratic forms - Asher Auel

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2020 - Conference Videos

From Hamilton’s Quaternions to Graves & Cayley’s Octonions – Louis Kauffman

We describe geometric and topological approaches to Hamilton's Quaternions and to the Octonions of Graves and Cayley.

From playlist G4G12 Videos

History of Science and Technology Q&A (June 2, 2021)

Stephen Wolfram hosts a live and unscripted Ask Me Anything about the history of science and technology for all ages. Originally livestreamed at: https://twitch.tv/stephen_wolfram/ Outline of Q&A 0:00 Stream starts 2:35 Stephen begins the stream 3:07 What appeared first in math, complex

From playlist Stephen Wolfram Ask Me Anything About Science & Technology

Guy Steele: A Logical Concern

From playlist A Celebration of CS at Harvard in Honor of Harry Lewis

Siggraph2019 Geometric Algebra

**Programmer focused part** starts at 18:00 Try the examples here https://enkimute.github.io/ganja.js/examples/coffeeshop.html The Geometric Algebra course at Siggraph 2019. Intro : Charles Gunn (00:00 - 18:00) Course : Steven De Keninck (18:00 - end) Course notes, slides, software, disc

From playlist Bivector.net

The remarkable Dihedron algebra | Famous Math Problems 21b | N J Wildberger

This is the second video on this Famous Math Problem: How to construct the (true) complex numbers? What we really want to do is proceed completely precisely and algebraically, but with as much generality as possible. For that, the Dihedron algebra D is the key ingredient. This is a sister

From playlist Famous Math Problems

QED Prerequisites Geometric Algebra 24 Paravectors

In this lesson we discover yet another way to partition the components of a general multivector. In this method, the partitioning is entirely dependent on a choice of reference frame. That is \gamma_0 must be chosen and it represents the 4-velocity of an observer who is stationary in that

From playlist QED- Prerequisite Topics

Example of Quaternions

Matrix Theory: For the quaternion alpha = 1 - i + j - k, find the norm N(alpha) and alpha^{-1}. Then write alpha as a product of a length and a direction.

From playlist Matrix Theory