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.

What is the relationship between quaternions and the concept of rotation in four dimensions?

Explain the significance of the unit sphere in the context of quaternions.

What are the implications of quaternion multiplication being non-commutative in practical applications?

How does the multiplication of quaternions differ when considering left versus right multiplication?