Knot Invariant Explorer
Trefoil · Figure-eight · Torus knots · Cinquefoil
Knot invariants are quantities that remain unchanged under ambient isotopy (continuous deformation). The crossing number is the minimum crossings in any diagram. Writhe counts signed crossings. The Alexander polynomial Δ(t) distinguishes many knots by their topology — the trefoil has Δ(t) = t⁻¹−1+t, while the unknot has Δ(t) = 1.