The angle trisection problem You have an angle and you have a pen, paper, compass and a straight edge. You don't know how big the angle is, divide this angle into three equal part using only the material that is listed here? If not possible what other tool is needed (protractors are not allowed)?
 A: As was already noted in comments, the problem admits no solution using compass and straight edge. You can render the problem solvable by either allowing neusis or tomahawk. 
Here I will explain the Archimedes solution using neusis. 

Given an angle $\alpha$, draw a circle centered at its tip point $\mathbf{O}$. Draw a chord $\mathbf{AC}$. Let $\beta = \angle \mathbf{BOC}$, and let  $\gamma = \angle \mathbf{BCO}$. 
It follows elementary that $\angle \mathbf{OBA} = \beta+\gamma$ and $\angle \mathbf{OAB} = \alpha - \gamma$. Since $\mathbf{OA} = \mathbf{OB}$ as radii,  $ \alpha - \gamma = \beta+\gamma$, giving $\gamma = \frac{\alpha - \beta}{2}$. If we further impose $\beta = \gamma$, we get $\beta=\gamma=\frac{\alpha}{3}$. 
In this configuration, $\mathbf{CB} = \mathbf{OB}$ as sides opposite to equal angles, which is how the neusis comes in. 
One would use the marked ruler, to make $\mathbf{CB}$ equal to the radius of the circle. 
A: The wording suggests a riddle, it can be done if you are allowed to fold the paper, so: LINK_1 and: LINK_2
