Definition:Intrinsic Equation

Definition
Let $C$ be a curve.

An intrinsic equation of $C$ is an equation that defines $C$ using a relation between the intrinsic properties of $C$.

Thus an intrinsic equation defines the shape of $C$ without specifying its position relative to an arbitrarily defined coordinate system.

Also known as
Some sources refer to the general intrinsic equation as a natural equation, but some prefer to reserve this term for the specific example where the intrinsic properties used are curvature and torsion.