>>1
I remember that I looked that up once for some reason. Oh well, maybe I'll look it up again some time.
Name:
Anonymous2007-12-20 0:30
ITT: people who don't belong on this forum. Unless they're just trolling -- then they're overqualified.
Name:
Anonymous2007-12-20 8:41
srsl gaiz, why do we peopl keep expanding number base? what problems wer unsolvable before and are solved with quaternions?
(troll to srsness ratio = 1:5, so pleaz answer)
Name:
Anonymous2007-12-20 14:56
>>5
Nothing. That's why we use vectors from the R3 vector space now with its cross product. It makes a normed linear space, essentially the same as R3.
Name:
Anonymous2007-12-20 17:08
quaternions do exactly the same thing as R3 vector space, cross products, and dot products. We'd probably be using quaternions now if they could have been manipulated such that multiplication with them was associative; the people messing around with them before we had good shit like R3 vector space etc were trying to get them to multiply associatively but they couldn't, thus leading to other stuff getting developed.
Quaternion multiplication is associative; they form a division ring. (A division ring is just a field whose multiplication might not be commutative.) What did you mean to say?
Name:
Anonymous2007-12-21 12:36
>>8
I think it's pretty safe to say >>7 has no fucking clue what he's talking about.
Name:
Anonymous2007-12-22 13:53
>>8
shit, I meant to so commutative not associative.
>>9
Its something that I vaguely remember from almost a year ago... some guy was trying to get commutative multiplication with quaternions and couldn't so he stop using them, and the people/person behind R3 vector space didn't care about not having commutative multiplication. Thus R3 vector space got used for stuff and quaternions didn't.
Name:
Anonymous2007-12-31 22:11
The thing that continues to bother me about quaternions is that algebraic equations have too many solutions. For example, consider x^2 + 1 = 0. Obviously, i, j, k, -i, -j, -k are all solutions. That's too many already, but it's not too bad.
But then you realize that (i cos t + j sin t) is also a solution for any real t at all, and you go totally insane.
Name:
Anonymous2007-12-31 23:30
>>11
Perhaps quaternion equations are best viewed as equations of four variables into a four dimensional space.
Name:
Anonymous2008-01-02 20:38
Quaternions, along with R^1, complex numbers, and octonions (Or Cayley Numbers) form the only normed algebras possible. Normed algebras of any other dimension are fail. So they're important in that respect.