Continuous symmetry
A symmetry that depends on a continuous parameter — the kind Noether's theorem turns into conservation laws.
Definition
A continuous symmetry is a transformation of a physical system that depends on a continuous parameter and leaves the dynamics unchanged. Translating an experiment by x metres is a continuous symmetry in x. Rotating it by θ radians is one in θ. Shifting the clock by Δt seconds is one in Δt. Each of these takes a continuous family of values, all of which leave the physics identical.
Noether's 1918 theorem is the statement that every continuous symmetry of a Lagrangian system has a conserved quantity attached to it. Time-translation → energy. Space-translation → momentum. Rotation → angular momentum. Discrete symmetries — like reflection or a 90° rotation of a square — do not yield conservation laws in the same way. The continuity is essential; it is what lets the symmetry be built up from infinitesimal pieces that the theorem can act on.