4 ms·

Check out the article "A Unified Mathematical Language for Physics and Engineering in the 21st Century" [0]. [0] http://geometry.mrao.cam.ac.uk/wp-content/uplo

• ajkjk 3y ago
  I.. don't think that has anything to do with their comment.
  • pizza 3y ago
    I thought they were asking about whether a coordinate system with basis elements e_1, e_2, ..., could be re-parameterized after rotation, and whether the re-parameterizations are infinite. The answer is simple via geometric algebra: yes. Given (* is geometric product, . is scalar product, ^ is wedge product) e_i * e_i = e_i . e_i + e_i ^ e_i = 1 + 0 = 1 e_i * e_j = e_i . e_j + e_i ^ e_j = 0 + -e_j ^ e_i = -(e_j * e_i) where the e_i are the basis elements along the infinite rays mentioned. To move to a rotated basis, make a rotor R = cos(theta/2) - e_i e_j sin(theta/2) ~R = cos(theta/2) + e_i e_j sin(theta/2) then you get the relationship in the new coordinate system: x' = R * x * ~R Since it's parameterized for any theta in [0..4pi], there's infinite of them, furthermore you get to pick which path you are taking to do the transformation along the way - either the 'negative' direction [0..2pi] or 'positive' direction [2pi..4pi]