There's a classic monography on the subject. Ivan Niven's "Irrational Numbers". Can't remember the publisher though....
My notation which I was using is called "Countinued Fraction". It is a topic in Number Theory. It is a truly remarkable topic in how to express any real number in terms of repeating nest of fraction. It is a theory that grew just because out of human fasination of expressing "ugly" irrationals as a beautiful patterns.
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