Mathematics
Optimization Problems with Constraints Using Lagrange Multipliers
Quick fact
The method of Lagrange multipliers transforms a constrained optimization problem into a system of equations by introducing a special variable λ (the Lagrange multiplier). The solution is found at points where the gradient of the objective function is parallel to the gradient of the constraint function.
Why this is interesting
You want to find the highest point on a hill, but you are only allowed to walk along a specific mountain trail. How can you know exactly where that highest point is?