## Vanity press: Exploring physics with geometric algebra

August 27, 2023 math and physics play

I just printed a copy of my ancient notes compilations for geometric algebra and physics, a compilation of old blog posts, using kindle direct publishing.

Amazon author copies don’t seem to be available in Canada anymore, so I had to buy a regular copy (printed in Bolton, Ontario, Canada!), but did so my setting the price as low as possible on amazon.ca (about \$20 CAD each).  That means that I got bound and printed books, with 469+503 pages, in 8.5×11″ format for about \$40 (buying an author copy from the US amazon.com would have cost more after shipping and currency conversion.)  I don’t think that I could have gotten bound print copies that cheap at one of the St George copy houses that service the university.

Now that I have my copies, I’ll un-publish these from amazon, so that nobody buys them by mistake.  I just wanted a copy of each as a reference for myself (as I do refer to parts of them sometimes — like the Pauli matrix/GA-equivalents writeup.)

This leaves me with 9 active titles on amazon (one is my book, and the rest are all course notes.)

## Video: Spherical basis vectors in geometric algebra

I’ve made a new manim-based video with a geometric algebra application.

In the video, the geometric algebra form for the spherical unit vectors are derived, then unpacked to find the conventional vector algebra form. We will then use our new tools to find the expression for the kinetic energy of a particle in spherical coordinates.

Prerequisites: calculus (derivatives and chain rule), complex numbers (exponential polar form), and geometric algebra basics (single sided rotations, vector multiplication, vector commutation sign changes, …)

You can find the video on Google’s censorship-tube, or on odysee.

## Geometric algebra: a very short video introduction.

Here’s another geometric algebra video, weighing in at a massive 2:29 (minutes.)

This video is a very short introduction to geometric algebra, showing the most basic concepts and how to apply them to the 2D geometric algebra of the Euclidean plane. Those concepts aren’t developed further in this video, but the idea is just to show the most basic consequences of the definitions.

Prerequisites: basic vector algebra (basis, vector space, dot product space, arrow representation of vectors, graphical vector addition, …)

If you watched yesterday’s video, don’t both watching this one, since it is extracted from that with no additions.

You can find the video on Google’s censorship-tube, and on odysee.