mod07lec40 - Discriminants, Galois groups of polynomials

Discriminants, quadratic and cubic polynomials are solvable, S_n, A_n

[hyperduality]

Even is dual to odd -- permutations.
Orbits (rotations) are dual to stabilizers (reflections).
Two reflections (mirrors or lines, axis) = a rotation (points).
Points are dual to lines -- the principle of duality in geometry.
Red relativistic geometry is dual to green relativistic geometry synthesizes blue relativistic geometry (Euclidian geometry) -- Chromogeometry.
Positive curvature (synchronic lines) is dual to negative curvature (enchronic lines) -- Gauss, Riemann geometry.
Hyperbolic geometry is dual! -- red & green.
Curvature and hence gravitation is dual.