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The aim of this paper is to show that Plato's theory of knowledge of Forms(intelligible Beings, Ideas) in the Sophistes, obtained by Division andCollection, is a close philosophic analogue of the geometric theory of periodicanthyphairesis, an ancient theory of incommensurability (developed by thePythagoreans, Theodorus and Theaetetus) having its modern counterpart in thetheory of continued fractions. Division corresponds to infinite anthyphaireticdivision, Collection to the Logos Criterion, resulting in periodicity and aself-similar One, precisely the One of a Platonic Form.

Plato's theory of knowledge of Forms by Division and Collection in the  Sophistes is a philosophic analogue of periodic anthyphairesis (and modern  continued fractions)