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Mathematics

Power Series and Taylor Expansion of Functions

Quick fact

Taylor series can compute functions like sine, cosine, and exponential to high accuracy using only arithmetic operations—addition, multiplication, and division—which is exactly what calculators and computers do.

Why this is interesting

Ever wondered how your calculator finds the sine of 30° without consulting a table? The answer lies in an astonishing trick: any smooth function can be rewritten as an infinite polynomial.