Why half angle? θ/2? in spin or quaternion space? intuitive geometry

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Why Half Angle θ/2? in Spin or Quaternion Space? Intuitive Geometry Why Half Angle θ/2? in Spin or Quaternion Space? Intuitive Geometry
Quaternions and 3d rotation, explained interactively Quaternions and 3d rotation, explained interactively
Demonstration of Spin 1/2 Demonstration of Spin 1/2
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Pre-geometry described in terms of quaternion spinors Pre-geometry described in terms of quaternion spinors
How quaternions produce 3D rotation How quaternions produce 3D rotation
Understanding Quaternions through Geometric Algebra Understanding Quaternions through Geometric Algebra
Visualizing the 4d numbers Quaternions Visualizing the 4d numbers Quaternions