Is there a conventional name for the set of rationals closed under taking square roots? It's not ℝ because it doesn't include the transcendentals, and it doesn't include things like ∛2.

@christianp You might have better luck finding a name for the Galois group? It should have a very particular structure - every element generates a subgroup of size a power of two, I think?

@anne @christianp Wikipedia says the members of this field are called the constructible numbers: en.wikipedia.org/wiki/Construc

You can also call it the quadratic closure of the rationals.

@11011110 @christianp Ah, thanks! I knew about the constructible numbers but I thought you could do more than just square roots with Euclidean geometry.

Interestingly, formalized origami allows you to produce non-constructible numbers; it is more powerful than Euclidean geometry in this sense.

@christianp I think these are the constructable numbers.

@christianp sorry. Didn't see the other responses you got before I posted.

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