The Rotation Problem and Hamilton's Discovery of Quaternions - Part 2 - Famous Math Problems 13b

Delve into the fascinating world of three-dimensional rotations and Hamilton's quaternions in this second lecture of a three-part series. Explore the geometry of spheres, composition of planar rotations, and the relationship between reflections and rotations. Learn about vectors, dot products, and cross products as you build a foundation for understanding quaternions. Discover Euler's theorem on rotation composition and a unique method of adding spherical vectors for visualizing rotation combinations. This in-depth exploration prepares you for the final lecture on Hamilton's quaternions and their practical applications in graphics, video games, and aerospace engineering.

Introduction to rotations and their composition-
Rotations of 3-Dimensional space geometrically
Planar situation
Algebra of planar rotations
Rotation of 3D space as a product of 2 reflections
Algebra of 3D Rotations about 0
Euler theorem - The product of two rotations is a rotation
The analytic approach via Linear Algebra
How to define 2 directions to be perpendicular; vectors
Cross product of 2 vectors