I’ve seen quaternions in an essay type video about imaginary numbers and it comes up quite a bit in game dev? What does it even mean.
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A quaternion is a number of the form a+bi+cj+dk, where a,b,c,d are reals (or any other type of number) and i,j,k are formal(!) imaginary units. This is a 4-dimensional thing, as there are 4 parameters to pick. They are added in the “intuitive” way and multiplication comes from i² = j² = k² = -1, i·j = k = -j·i, j·k = i = -k·j, k·i = j = -i·k. Maybe unintuitively for the layman, this is not _commutative_ as i·j and j·i give different results. However:
Multiplication by quaternions with a²+b²+c²+d² = 1 can be interpreted as rotations of the entire 4-dimensional space, and setting a=0 as well then as rotations in 3 dimensions; i.e. something arising in computer graphics very often. This also explains why commutativity is not really an option then: two rotations around skew axes do not commute, as one can easily check by consecutively rotating either a ball (or even better a Rubik’s cube) by 90° along two orthogonal axes.
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