Geometric Constructible Numbers

[emptyboat]

Geometric Constructible Numbers...

Hi, everyone.
I have a question about geometric constructible numbers.
I know that "if 'a' is constructible then [Q(a):Q]=2^n."
But I heard that its inverse is not true.
I want some counter examples about the inverse statement.
(I have checked by googling 'i' is a constructible number.)

Help...

 

[HallsofIvy]

You mean you want a number that is algebraic of order a power of 2 and is NOT a constructible number? Hmm, now thats' a good question! I will need to think about that- for a few decades.

 

[emptyboat]

Yes, I mean that.
So, there was no clear answer about that?