Gradient of curve? (Langrangian multipliers)

[Pelleman]

I dont understand the usage of the word gradient often used in the explanation of lagrangian multipliers.
Say you seek the maximum of some function f(x,y) given the constraint G(): x^2+y^2 = 3.
since the constrant is just a curve how could one get "gradient" of it. Sounds a bit irregular...
I understand the rest of the idea, just not the "gradient" of a curve.

 

[Romsek]

you take the gradient of [MATH]f(x,y) - \lambda (g(x,y)-C)[/MATH]
where $\displaystyle C$ is what your constraint function is constrained to equal and $\displaystyle \lambda$ is the Lagrange multiplier.

The gradient is taken with respect to $\displaystyle (x,y,\lambda)$ and the the result of differentiating w/respect to $\displaystyle \lambda$
just gets you the constraint term of the original problem.