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Mathematics

Rational Approximations to Real Numbers via Continued Fractions

Quick fact

The continued fraction expansion of any real number provides the best rational approximations possible: each convergent is closer than any other fraction with a smaller or equal denominator.

Why this is interesting

You know 22/7 is close to π, but what if I told you there's a truly optimal way to find such fractions—and it's linked to how numbers are built?