Introduction to RAU
Quadrant-aware modular arithmetic - RAU maps a linear parameter (0–4) to a circle using integer and fractional parts.
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Diagonal Derivation
Visual proof: How RAU formulas emerge from diagonal parameterization
Point on Diagonal:
(1-t, t) = (0.500, 0.500)
Distance r: √(1 - 2t + 2t²) = 0.707
On Unit Circle:
rcos = (1-t)/r = 0.707
rsin = t/r = 0.707
Angle: 45.0°
(1-t, t) = (0.500, 0.500)
Distance r: √(1 - 2t + 2t²) = 0.707
On Unit Circle:
rcos = (1-t)/r = 0.707
rsin = t/r = 0.707
Angle: 45.0°
Radical Angle Unit as: |cross| / (|cross| + |dot|)
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30°
100
90°