The Spiral of Theodorus

Spiral of Theodorus Source: https://commons.wikimedia.org/wiki/File:Spiral_of_Theodorus.svg
The root spiral of Theodorus Source

In Plato’s dialogue, Theaetetus (p. 147d), there is a cryptic description of a complicated geometrical diagram that the geometrician, Theodorus, drew for his students. Down through the centuries there has been much speculation about exactly what Theodorus was supposed to have drawn.

We know that it involved the roots of square areas in the natural number series up the area of 17, and so √17. But then at √17 Theodorus stopped, so we are told, because after that the diagram got ‘entangled’ (enescheto).

What happened after √17?

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