4 ms·

I feel like Geometric algebra / clifford algebra is something more people should know. It makes N-dimensional vector algebra easier and more intuitive.

thelastbender12 8y ago
could you recommend a good source to pick it?
- layoutIfNeeded 8y ago
  Geometric Algebra For Computer Science, An Object Oriented Approach to Geometry, published by Morgan Kaufmann Publishers http://geometricalgebra.net http://geometricalgebra.net David Hestenes: New Foundations for Classical Mechanics https://www.amazon.com/Foundations-Classical-Mechanics-Fundamental-Theories/dp/0792353021 https://www.amazon.com/Foundations-Classical-Mechanics-Funda... Geometric Algebra on euclideanspace.com by Martin John Baker: http://www.euclideanspace.com/maths/algebra/clifford/index.htm http://www.euclideanspace.com/maths/algebra/clifford/index.h...
- nimish 8y ago
  Linear and geometric algebra Vector and geometric calculus Both by Alan macdonald, both very good.
- msla 8y ago
  Edit: Better link: https://www.av8n.com/physics/clifford-intro.htm https://www.av8n.com/physics/clifford-intro.htm https://www.av8n.com/physics/spacetime-welcome.htm https://www.av8n.com/physics/spacetime-welcome.htm
- jacobolus 8y ago
  What is your background/perspective? For introductory motivation, check out https://www.shapeoperator.com/2016/12/12/sunset-geometry/ https://www.shapeoperator.com/2016/12/12/sunset-geometry/ And perhaps follow up with the GA for Computer Science book, or if you like (or want to learn about) Newtonian mechanics, try Hestenes’s book New Foundations for Classical Mechanics. For people with a mathier background, I would recommend https://arxiv.org/abs/1205.5935 https://arxiv.org/abs/1205.5935
  - thelastbender12 8y ago
    thank you, this looks interesting. The parent comment caught my eye since I'm pretty comfortable visualizing linear algebra with 2D arrays but struggle beyond that.
jacobolus 8y ago
There is a relationship between GA and Octonions (and the 7-dimensional “cross product”). http://www.math.ucr.edu/home/baez/octonions/node7.html http://www.math.ucr.edu/home/baez/octonions/node7.html
Ericson2314 8y ago
So glad this is the first comment. https://arxiv.org/abs/1401.2371 https://arxiv.org/abs/1401.2371 for ultimate contrarian math.
- dan-robertson 8y ago
  What is contrarian about it? I realise that this approach isn’t super commonly used but I don’t think it’s popularly considered to be a bad or wrong way to do things
  - yiyus 8y ago
    NJ Wildberger, who is behind rational trigonometry, has some radical ideas. However, I do not think there is anything wrong with his results (at least most of them, his videos are great too!) and most of them could probably be applied in a more formal framework. In my opinion, this paper is a good example.

thelastbender12 8y ago

could you recommend a good source to pick it?

layoutIfNeeded 8y ago
Geometric Algebra For Computer Science, An Object Oriented Approach to Geometry, published by Morgan Kaufmann Publishers http://geometricalgebra.net http://geometricalgebra.net David Hestenes: New Foundations for Classical Mechanics https://www.amazon.com/Foundations-Classical-Mechanics-Fundamental-Theories/dp/0792353021 https://www.amazon.com/Foundations-Classical-Mechanics-Funda... Geometric Algebra on euclideanspace.com by Martin John Baker: http://www.euclideanspace.com/maths/algebra/clifford/index.htm http://www.euclideanspace.com/maths/algebra/clifford/index.h...
nimish 8y ago
Linear and geometric algebra Vector and geometric calculus Both by Alan macdonald, both very good.
msla 8y ago
Edit: Better link: https://www.av8n.com/physics/clifford-intro.htm https://www.av8n.com/physics/clifford-intro.htm https://www.av8n.com/physics/spacetime-welcome.htm https://www.av8n.com/physics/spacetime-welcome.htm
jacobolus 8y ago
What is your background/perspective? For introductory motivation, check out https://www.shapeoperator.com/2016/12/12/sunset-geometry/ https://www.shapeoperator.com/2016/12/12/sunset-geometry/ And perhaps follow up with the GA for Computer Science book, or if you like (or want to learn about) Newtonian mechanics, try Hestenes’s book New Foundations for Classical Mechanics. For people with a mathier background, I would recommend https://arxiv.org/abs/1205.5935 https://arxiv.org/abs/1205.5935
- thelastbender12 8y ago
  thank you, this looks interesting. The parent comment caught my eye since I'm pretty comfortable visualizing linear algebra with 2D arrays but struggle beyond that.

jacobolus 8y ago

There is a relationship between GA and Octonions (and the 7-dimensional “cross product”). http://www.math.ucr.edu/home/baez/octonions/node7.html http://www.math.ucr.edu/home/baez/octonions/node7.html

Ericson2314 8y ago

So glad this is the first comment. https://arxiv.org/abs/1401.2371 https://arxiv.org/abs/1401.2371 for ultimate contrarian math.

dan-robertson 8y ago
What is contrarian about it? I realise that this approach isn’t super commonly used but I don’t think it’s popularly considered to be a bad or wrong way to do things
- yiyus 8y ago
  NJ Wildberger, who is behind rational trigonometry, has some radical ideas. However, I do not think there is anything wrong with his results (at least most of them, his videos are great too!) and most of them could probably be applied in a more formal framework. In my opinion, this paper is a good example.