1/? My article "Teaching Magnetism with Bivectors" was just published as the December cover article of the American Journal of Physics. I've talked about my bivector work before, but with lots of new people here, maybe this is a new excuse to share. 🎢🧪 #ITeachPhysics pubs.aip.org/aapt/ajp/art... - ThreadSky

steuard.bsky.social • 97 days ago

1/? My article "Teaching Magnetism with Bivectors" was just published as the December cover article of the American Journal of Physics. I've talked about my bivector work before, but with lots of new people here, maybe this is a new excuse to share. 🎢🧪 #ITeachPhysics
https://pubs.aip.org/aapt/ajp/article-abstract/92/12/936/3321383/Teaching-magnetism-with-bivectors

Comments

randallphysics.bsky.social•94 days ago

I watched your video and I really like this method. I used to teach AP Physics C, this would be really interesting to try in that course, or in AP 1.

thewjp.bsky.social•97 days ago

Who needs an excuse?

steuard.bsky.social•97 days ago

2/? Quick summary: Rotational and magnetic quantities that we traditionally express as vectors are better described as *bivectors*, drawn as oriented tiles rather than as arrows. Unfamiliar? Sure. But this has benefits for novices and experts.

[This doesn't require geometric algebra, by the way.]

stijnoomes.bsky.social•65 days ago

I enjoyed your bivector story. Thanks!

What do you use to create those beautiful 3D illustrations?

steuard.bsky.social•65 days ago

The 3D magnetic field tile images were made with Mathematica. (I'm right in the middle of writing up the routines for it in a shareable form.)

steuard.bsky.social•97 days ago

3/? Intro: Most quantities in physics are one of two types. A *vector* has a magnitude in a specific direction (think "velocity" or "force", often represented by an arrow) while a *scalar* has no implied direction (think "mass" or "temperature"). But sometimes, our "vector" label is a bit of a fib.

steuard.bsky.social•97 days ago

4/? A rotating object (like a merry-go-round or a ball on a string) has "angular velocity" at some angle in space, but it doesn't feel like a vector: rotation happens in a *plane*. So we use a "right-hand rule": curl your fingers with the rotation, and your thumb shows the angular velocity vector 𝜔.

steuard.bsky.social•97 days ago

5/? Right-hand rules also arise any time you work with magnetic fields. For example, when electric current flows around a loop, it generates a magnetic field whose direction through the loop is given by curling your fingers around with the current: your thumb indicates the magnetic field inside.

steuard.bsky.social•97 days ago

6/? But right-hand rules are tricky and nonintuitive for beginners, they only work in 3D (no simple 2D examples; no relativistic spacetime), and the resulting vectors aren't quite vectors at all: they mysteriously reverse if you look at the system in a mirror.

Using bivectors makes all this better.

steuard.bsky.social•97 days ago

7/? A *bivector* is the natural two-dimensional geometric quantity: instead of an arrow, you can visualize it as a tile whose area represents magnitude, tilted at a given angle, and with an orientation (clockwise/counterclockwise). (Shape doesn't matter.) Very intuitive for describing rotations!

ataleortwo.bsky.social•97 days ago

I’ll said it again, the world is alive with eddies.

And it looks like magnetic fields are no different.

Congrats on the publication!

jdidaleusky.bsky.social•97 days ago

Sweet

jdidaleusky.bsky.social•97 days ago

I have physics ?’s. I have so ideas about the how the math can show a physical truth but confound us all. I would enjoy a conversation. Cheers

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