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Mathematics

Taylor Series: Approximating Functions with Polynomials

Quick fact

The Taylor series can approximate any smooth function to any desired accuracy by including enough terms—no matter how complex the function, it can be reduced to simple algebra.

Why this is interesting

You've probably punched sin(x) into a calculator without thinking—but how does it actually compute that? It doesn't use a circle; it uses a polynomial that mimics the sine wave, based on a Taylor series.