Constructible Length with Compass and Straightedge

Theorem
Let $L$ be a line segment in a Eucldiean space.

Let the length of $L$ be $d$.

Let $L'$ be a line segment of length $d'$ constructed from $L$ using a compass and straightedge construction.

Then:
 * $d' = q d$

where $q$ is an algebraic number whose degree is a power of $2$.