Mathematics
Taylor Series for Approximating Common Transcendental Functions
Quick fact
The Taylor series for e^x centered at 0 is 1 + x + x²/2! + x³/3! + ..., and just four terms give an error of less than 0.01 for x between -1 and 1. These series are not just approximations—they are exact when infinitely many terms are used.
Why this is interesting
You've probably used a calculator to find sin(0.5) or e^2, but how does it actually compute these values? The answer lies in a surprising idea: replace the function with a polynomial.