Mathematics
Numerical Methods for Approximating Definite Integrals: Simpson's Rule
Quick fact
Simpson's rule is so effective that for many functions it gives exact results for polynomials up to degree 3, while the trapezoidal rule is exact only for linear functions.
Why this is interesting
If a function has no elementary antiderivative, how can we still find the area under its curve? Simpson's rule provides an elegant numerical shortcut that often gives astonishingly accurate results.