Home▸Mathematics▸Galois Theory: Root Permutations & Solvability in Radicals Simulator

🔀 Galois Theory: Root Permutations & Solvability in Radicals Simulator

Interactive Galois theory visualizer: polynomial roots plotted on a complex plane, with the Galois group's permutations animated as symmetric exchanges of the roots, and a live solvable-by-radicals check for degree 3-5 polynomials.

Mathematics3DAdvanced60 FPS

Details

CategoryMathematics

RenderingThree.js · WebGL

DifficultyAdvanced

Target FPS60

ControlsPreset dropdown picks a degree-3 (editable via p,q sliders), degree-4 or degree-5 polynomial; clicking a Galois-group permutation button (shown in cycle notation) animates the roots swapping positions; toggles show/hide the root-connecting polygon and the numeric root labels.

Three.jsGalois theoryabstract algebracomplex rootsDurand-Kernergroup theory

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⚙ Under the hood

Plots the complex roots of a degree 3-5 polynomial on the complex plane and animates the Galois group's permutations as symmetric exchanges of those roots. Compares solvable groups (C3, S3, D4, C4, F20) against the non-solvable S5 of x^5-4x-2, the classic Abel-Ruffini example with no radical formula.

Three.jsGalois theoryabstract algebracomplex rootsDurand-Kernergroup theory

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install