Mostafa Sayyah @Mostafa_S_Math
Joined October 2026-
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Mostafa Sayyah retweeted
In 1914, Srinivasa Ramanujan published Modular Equations and Approximations to π in the Quarterly Journal of Pure and Applied Mathematics. Among its intresting results was an infinite series containing four seemingly mysterious numbers: 1103, 26390, 396 and 9801. The formula is 1/π = (2√2/9801) ∑ₙ₌₀^∞ [(4n)!(1103 + 26390n) / ((n!)⁴ · 396⁴ⁿ)] Its wonderful property is the speed of convergence. Each additional term contributes roughly eight more decimal digits of accuracy.
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Mostafa Sayyah retweeted
Galois saw that every equation hides a group of symmetries and that group alone decides whether the roots can ever be written with radicals. The field ℚ(√2, i) and its three quadratic subfields correspond exactly to the subgroups of the Klein four-group. Blue labels mark the fixed fields; the lattice is the dictionary between algebra and geometry. For the quintic x⁵ − 4x + 2, Eisenstein shows it is irreducible and it has precisely three real roots. Complex conjugation therefore acts as a transposition, forcing the Galois group to be all of S₅. Since A₅ is simple, S₅ is not solvable, so the roots lie in no radical tower. Solvability is not about clever formulas. It is a structural property of the symmetry group.
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