PseuRanAcc

4 ms·

1. 1.▲
   by PseuRanAcc 8y ago

   Regarding the angle between (a-b) and b: you can repeat the process until you end up with two vectors that cannot be reduced with respect to one another. Eventually the angle will be between 60 and 120 degrees (because you can always negate
2. 2.▲
   by PseuRanAcc 8y ago

   Yes, using some linear algebra: - The inner product (or dot product) of two vectors is related to the angle (a,b) = |a| |b| cos(angle). - The cosine of 60 degrees is 1/2 (and it is increasing from 60 degrees to 0 degrees, where it is 1
3. 3.▲
   by PseuRanAcc 8y ago

   Technically these should be reduced to (1,-1), (1,2) and (2,-2), (1,3) which should have angles >60.
4. 4.▲
   by PseuRanAcc 8y ago

   This is something that has to do with Lattice basis reduction ( https://en.wikipedia.org/wiki/Lattice_reduction ). Rough explanation: if the angle is less than 60, then subtracting the smaller vector of the larger vector