>> Can anyone tell me where to find examples of impossible >> constructions which lead to algebraic numbers of degree four >> (or, more generally, some power of 2)? > > Here's one: > > Construct a cyclic 10-gon with 9 sides of length 1 and > the remaining side of length 2. > > The radius r is a non-constructible number with algebraic > degree 8 over Q.
Thanks a lot. I was looking after examples such as this one and the one you mentioned after it.