The projective rational view of the 3D rotation group SO(3) | Classical to Quantum | Wild Egg Maths
Автор: Wild Egg Maths
Загружено: 2025-02-23
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Today we move towards a full projective view of the 3D rotation group SO(3) extending our Cayley transform / anchor approach, avoiding irrationalities (and the "exponential map") and utilizing basic ideas from Projective Geometry. These are introduced via homogeneous coordinates for planar curves.
We will obtain formulas that connect with 19th century work of Olinde Rodrigues, but are framed without angles, instead relying on Rational Trigonometry (ie quadrances and spreads). The results can be completed exhibited with explicit examples entirely over the rational numbers. We are very close to discovering quaternions here!
This is part of the Classical to Quantum series, where we look at aspects of foundational modern physics from a mathematical point of view.
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