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Note don't to be confused with Algebraic Geometry they are different; When I first came across this topic it was eye opening, especially the fact that you coul
by user070223 2y ago
Note don't to be confused with Algebraic Geometry they are different;
When I first came across this topic it was eye opening, especially the fact that you could squeeze Maxwell's equations into one and the fact that pseudovector create by cross product from physics is just a bivector which in 3d could be represented like a vector orthogonal to the plane created by the two vectors in the product
Primer on the topic https://www.youtube.com/watch?v=60z_hpEAtD8 https://www.youtube.com/watch?v=60z_hpEAtD8 (And other videos on his channel)
Another greate playlist is https://www.youtube.com/watch?v=0VGMxSUDBH8&list=PLLvlxwbzkr7igd6bL7959WWE7XInCCevt&index=1 https://www.youtube.com/watch?v=0VGMxSUDBH8&list=PLLvlxwbzkr...
BTW the author has the following page https://projectivegeometricalgebra.org/ https://projectivegeometricalgebra.org/ with great infographics and references
- BenoitP 2y agoHah! I knew Sudgy would be your first link. There's relatively little content about GA, but once you're hooked you begin to consume it all. It's like you never got to study Relativity, conformal geometry, electron spins, quaternions, etc then someone comes with a simple cheat code which introduces you to these topics gently. It's like what category theory wants to do for mathematics, but simple. Here are additional resources: GA playground: https://enkimute.github.io/ganja.js/examples/coffeeshop.html#pga2d_points_and_lines https://enkimute.github.io/ganja.js/examples/coffeeshop.html... A physics engine in 100 lines (Gravity, Hook, and damping laws are just one line each!), and you can go from 2D to 3D to 4D by changing a single parameter: https://enki.ws/ganja.js/examples/pga_dyn.html https://enki.ws/ganja.js/examples/pga_dyn.html Other resources: https://bivector.net/ https://bivector.net/ And anything by David Hestenes: https://worrydream.com/refs/Hestenes_2002_-_Reforming_the_Mathematical_Language_of_Physics.pdf https://worrydream.com/refs/Hestenes_2002_-_Reforming_the_Ma...
- deleted 2y ago[deleted]
- gowld 2y agoThe absolute first video to watch should be the (ironically titled) Why can't you multiply vectors? https://www.youtube.com/watch?v=htYh-Tq7ZBI https://www.youtube.com/watch?v=htYh-Tq7ZBI
- Certhas 2y agoNote though that GA is extremely niche and offers very little beyond exterior algebra. Exterior algebra in the context of differential forms is standard part of the postgrad (and sometimes undergrad) Physics curriculum. See the applications to physics section here: https://en.m.wikipedia.org/wiki/Differential_form https://en.m.wikipedia.org/wiki/Differential_form