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

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This lecture explores geometric and algebraic ways to describe and compose three-dimensional rotations. It covers Euler’s theorem, rotations as products of reflections, and vectors with the dot and cross products.

Syllabus

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

Taught by

Insights into Mathematics

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