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Many many fascinating properties

Enough material for several colloquium talks

Connections with:

Euclid's algorithm

Farey series

Fibonacci numbers

Möbius transformations

Measure theory

Stern-Brocot representation

We will have to content ourselves with just a few of the most important properties

Every real number has a (nearly) unique continued fraction representation

The representation is finite if and only if the number is rational

Simple rationals have representations with few terms and small terms

It's easy to decide which of two continued fractions represents the larger number

Truncating the representation of

*a*gets you a*very good*rational approximation to*a*

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