While a phone or arrow turns all the way around in 360 degrees, the quaternion describing this 360-degree rotation only turns 180 degrees up in four-dimensional space.

The mathematical properties of unit quaternions (those with length equal to 1) make them ideal for representing rotations in three dimensions.

IN a paper by Prof. C. G. Knott on “Recent Innovations in Vector Theory,” of which an abstract has been given in NATURE (vol. xlvii. pp. 590–593; see also a minor abstract on p. 287), the ...

This paper examines the mathematical modelling of rigid origami, a type of origami where all the panels are rigid and can only rotate about crease lines. The rotating vector model is proposed, which ...