Linking Number
Configuration:
Hopf link (lk=1)
Unlinked (lk=0)
Trefoil+circle (lk=2)
Double link (lk=2)
Speed:
0.5
Tube radius:
0.12
lk =
1
The Gauss linking integral lk(α,β) = (1/4π) ∮∮ (α(s)−β(t))·(α'(s)×β'(t)) / |α(s)−β(t)|³ ds dt counts algebraic intersections of one curve with a surface bounded by the other. It is a topological invariant: an integer unchanged by smooth deformation.