Visualizing quaternions (4d numbers) with stereographic projection - Part 1 of 2

The video explores quaternions, a 4D extension of complex numbers, and their applications in 3D rotations and quantum mechanics. It covers the history of their discovery by Hamilton, their resurgence in computing, and their mathematical properties. The video also explains complex numbers and stereographic projection to help visualize quaternions in 4D space, emphasizing their non-commutative nature and unique multiplication properties.

What are quaternions and how do they relate to complex numbers?

Describe the significance of William Rowan Hamilton's discovery of quaternions.

Explain how quaternions are used in computer graphics and robotics.

What is the relationship between quaternions and quantum mechanics?

How does the stereographic projection help in visualizing quaternions?

How can quaternions be represented in four-dimensional space?

What are the key differences between quaternion multiplication and complex number multiplication?

What is the role of the right-hand rule in understanding quaternion rotations?

Discuss the concept of non-commutativity in quaternion multiplication.

Explain the process of conjugation in relation to quaternion multiplication.