Quaternions Unraveled: Rotations, SU(2), and the Geometry of 3D

Trace quaternions from Hamilton’s 1843 breakthrough to their modern power in 3D rotations, computer graphics, and robotics. We unpack unit quaternions, the non-commutative magic that encodes orientation, and the double-cover phenomenon. Explore how quaternions connect to spherical trigonometry (via Terence Tao) and the SU(2) link, with practical glimpses like the sunrise equation. A deep dive into why this elegant 4D tool reshapes our understanding of geometry and motion.

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