What are quaternions, and how do you visualize them? A story of four dimensions.

The video explores quaternions, a four-dimensional extension of complex numbers, and their applications in 3D rotations and quantum mechanics. It covers the historical discovery by William Rowan Hamilton and their resurgence in modern computing. The video also explains quaternion multiplication, visualizing them in 4D space, and their non-commutative nature. Through stereographic projection, viewers learn to understand quaternions' geometric properties and their role in describing rotations.

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