im reading a book on quaternions by vince jones at the moment that basically says we are using quaternions now because they "just happen" to encode an axis-angl

im reading a book on quaternions by vince jones at the moment that basically says we are using quaternions now because they "just happen" to encode an axis-angle rotation in their algebra. thats it! theres no more magic than that. just like complex numbers encode a rotation in 2d due to the way the algebra is structured. olinde rodrigues wrote about axis-angle rotations before hamilton discovered quaternions, and i think euler and gauss may have been involved too. anyway, its a fascinating story about the meeting of algebra and geometry.