Rational 3D rotation theory - the reveal! | Classical to Quantum | Wild Egg Maths
Автор: Wild Egg Maths
Загружено: 2025-01-25
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In this video we present an alternative, purely rational or algebraic view of the theory of rotations in 3D space, through a single example where exciting new formulas and concepts arise. This is not a thorough treatment of this new development, but rather a showcase of what it looks like in a way that may be appreciated by anyone with some basic knowledge of linear algebra.
We avoid angles and circular functions (cos, tan etc) as well as "irrational numbers" like "pi" and "e". Instead we take some very basic notions from Rational Trigonometry and combine them with elementary matrix algebra and the geometry of 3D space coming from the usual symmetric bilinear form, or dot product.
The important relation between a rotation \rho in SO(3) and its "anchor" A in so(3) which emerges is the central feature.
This new technology has the potential to seriously transform not just Lie theory and attendant harmonic analysis / representation theory, but also the adjacent areas of physics where symmetries, along with computation packages / software that utilize the algebra of 3D rotations. (Blender, Maya, AutoCad, Mathematica, Matlab etc ).
We will be developing this theory in more detail in subsequent videos. Many new additional features will emerge, so this is very exciting. Please join us in this adventure: "Classical to Quantum."
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